Content-Type: multipart/mixed; boundary="-------------0307030342736" This is a multi-part message in MIME format. ---------------0307030342736 Content-Type: text/plain; name="03-317.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="03-317.keywords" Critical prewetting, entropic repulsion, wetting, pinning, effective interface models, Ising model ---------------0307030342736 Content-Type: application/postscript; name="V03.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="V03.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.92b Copyright 2002 Radical Eye Software %%Title: prewetting1.dvi %%Pages: 30 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: CMR17 CMR12 CMTT12 CMBX9 CMR9 CMBX12 CMR10 CMMI10 CMMI7 %%+ CMSY10 CMR7 CMEX10 CMSY7 CMMI5 CMSS10 MSBM7 CMSL8 MSBM10 CMBX10 %%+ CMTI10 CMSY5 CMR5 CMSS8 TeX-cmex7 CMSL10 MSAM10 CMMI12 CMBX7 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips -o V03.ps prewetting1.dvi %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2003.07.03:1032 %%BeginProcSet: texc.pro %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3 1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{ rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B /chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{ /cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{ A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse} ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17 {2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{ 1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop} forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: texps.pro %! TeXDict begin/rf{findfont dup length 1 add dict begin{1 index/FID ne 2 index/UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]FontType 0 ne{/Metrics exch def dict begin Encoding{exch dup type/integertype ne{ pop pop 1 sub dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get div def}ifelse}forall Metrics/Metrics currentdict end def}{{1 index type /nametype eq{exit}if exch pop}loop}ifelse[2 index currentdict end definefont 3 -1 roll makefont/setfont cvx]cvx def}def/ObliqueSlant{dup sin S cos div neg}B/SlantFont{4 index mul add}def/ExtendFont{3 -1 roll mul exch}def/ReEncodeFont{CharStrings rcheck{/Encoding false def dup[ exch{dup CharStrings exch known not{pop/.notdef/Encoding true def}if} forall Encoding{]exch pop}{cleartomark}ifelse}if/Encoding exch def}def end %%EndProcSet %%BeginProcSet: special.pro %! TeXDict begin/SDict 200 dict N SDict begin/@SpecialDefaults{/hs 612 N /vs 792 N/ho 0 N/vo 0 N/hsc 1 N/vsc 1 N/ang 0 N/CLIP 0 N/rwiSeen false N /rhiSeen false N/letter{}N/note{}N/a4{}N/legal{}N}B/@scaleunit 100 N /@hscale{@scaleunit div/hsc X}B/@vscale{@scaleunit div/vsc X}B/@hsize{ /hs X/CLIP 1 N}B/@vsize{/vs X/CLIP 1 N}B/@clip{/CLIP 2 N}B/@hoffset{/ho X}B/@voffset{/vo X}B/@angle{/ang X}B/@rwi{10 div/rwi X/rwiSeen true N}B /@rhi{10 div/rhi X/rhiSeen true N}B/@llx{/llx X}B/@lly{/lly X}B/@urx{ /urx X}B/@ury{/ury X}B/magscale true def end/@MacSetUp{userdict/md known {userdict/md get type/dicttype eq{userdict begin md length 10 add md maxlength ge{/md md dup length 20 add dict copy def}if end md begin /letter{}N/note{}N/legal{}N/od{txpose 1 0 mtx defaultmatrix dtransform S atan/pa X newpath clippath mark{transform{itransform moveto}}{transform{ itransform lineto}}{6 -2 roll transform 6 -2 roll transform 6 -2 roll transform{itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll curveto}}{{closepath}}pathforall newpath counttomark array astore/gc xdf pop ct 39 0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack} if}N/txpose{pxs pys scale ppr aload pop por{noflips{pop S neg S TR pop 1 -1 scale}if xflip yflip and{pop S neg S TR 180 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip yflip not and{pop S neg S TR pop 180 rotate ppr 3 get ppr 1 get neg sub neg 0 TR}if yflip xflip not and{ppr 1 get neg ppr 0 get neg TR}if}{ noflips{TR pop pop 270 rotate 1 -1 scale}if xflip yflip and{TR pop pop 90 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip yflip not and{TR pop pop 90 rotate ppr 3 get ppr 1 get neg sub neg 0 TR}if yflip xflip not and{TR pop pop 270 rotate ppr 2 get ppr 0 get neg sub neg 0 S TR}if}ifelse scaleby96{ppr aload pop 4 -1 roll add 2 div 3 1 roll add 2 div 2 copy TR .96 dup scale neg S neg S TR}if}N/cp{pop pop showpage pm restore}N end}if}if}N/normalscale{ Resolution 72 div VResolution 72 div neg scale magscale{DVImag dup scale }if 0 setgray}N/psfts{S 65781.76 div N}N/startTexFig{/psf$SavedState save N userdict maxlength dict begin/magscale true def normalscale currentpoint TR/psf$ury psfts/psf$urx psfts/psf$lly psfts/psf$llx psfts /psf$y psfts/psf$x psfts currentpoint/psf$cy X/psf$cx X/psf$sx psf$x psf$urx psf$llx sub div N/psf$sy psf$y psf$ury psf$lly sub div N psf$sx psf$sy scale psf$cx psf$sx div psf$llx sub psf$cy psf$sy div psf$ury sub TR/showpage{}N/erasepage{}N/setpagedevice{pop}N/copypage{}N/p 3 def @MacSetUp}N/doclip{psf$llx psf$lly psf$urx psf$ury currentpoint 6 2 roll newpath 4 copy 4 2 roll moveto 6 -1 roll S lineto S lineto S lineto closepath clip newpath moveto}N/endTexFig{end psf$SavedState restore}N /@beginspecial{SDict begin/SpecialSave save N gsave normalscale currentpoint TR @SpecialDefaults count/ocount X/dcount countdictstack N} N/@setspecial{CLIP 1 eq{newpath 0 0 moveto hs 0 rlineto 0 vs rlineto hs neg 0 rlineto closepath clip}if ho vo TR hsc vsc scale ang rotate rwiSeen{rwi urx llx sub div rhiSeen{rhi ury lly sub div}{dup}ifelse scale llx neg lly neg TR}{rhiSeen{rhi ury lly sub div dup scale llx neg lly neg TR}if}ifelse CLIP 2 eq{newpath llx lly moveto urx lly lineto urx ury lineto llx ury lineto closepath clip}if/showpage{}N/erasepage{}N /setpagedevice{pop}N/copypage{}N newpath}N/@endspecial{count ocount sub{ pop}repeat countdictstack dcount sub{end}repeat grestore SpecialSave restore end}N/@defspecial{SDict begin}N/@fedspecial{end}B/li{lineto}B /rl{rlineto}B/rc{rcurveto}B/np{/SaveX currentpoint/SaveY X N 1 setlinecap newpath}N/st{stroke SaveX SaveY moveto}N/fil{fill SaveX SaveY moveto}N/ellipse{/endangle X/startangle X/yrad X/xrad X/savematrix matrix currentmatrix N TR xrad yrad scale 0 0 1 startangle endangle arc savematrix setmatrix}N end %%EndProcSet %%BeginProcSet: color.pro %! TeXDict begin/setcmykcolor where{pop}{/setcmykcolor{dup 10 eq{pop setrgbcolor}{1 sub 4 1 roll 3{3 index add neg dup 0 lt{pop 0}if 3 1 roll }repeat setrgbcolor pop}ifelse}B}ifelse/TeXcolorcmyk{setcmykcolor}def /TeXcolorrgb{setrgbcolor}def/TeXcolorgrey{setgray}def/TeXcolorgray{ setgray}def/TeXcolorhsb{sethsbcolor}def/currentcmykcolor where{pop}{ /currentcmykcolor{currentrgbcolor 10}B}ifelse/DC{exch dup userdict exch known{pop pop}{X}ifelse}B/GreenYellow{0.15 0 0.69 0 setcmykcolor}DC /Yellow{0 0 1 0 setcmykcolor}DC/Goldenrod{0 0.10 0.84 0 setcmykcolor}DC /Dandelion{0 0.29 0.84 0 setcmykcolor}DC/Apricot{0 0.32 0.52 0 setcmykcolor}DC/Peach{0 0.50 0.70 0 setcmykcolor}DC/Melon{0 0.46 0.50 0 setcmykcolor}DC/YellowOrange{0 0.42 1 0 setcmykcolor}DC/Orange{0 0.61 0.87 0 setcmykcolor}DC/BurntOrange{0 0.51 1 0 setcmykcolor}DC /Bittersweet{0 0.75 1 0.24 setcmykcolor}DC/RedOrange{0 0.77 0.87 0 setcmykcolor}DC/Mahogany{0 0.85 0.87 0.35 setcmykcolor}DC/Maroon{0 0.87 0.68 0.32 setcmykcolor}DC/BrickRed{0 0.89 0.94 0.28 setcmykcolor}DC/Red{ 0 1 1 0 setcmykcolor}DC/OrangeRed{0 1 0.50 0 setcmykcolor}DC/RubineRed{ 0 1 0.13 0 setcmykcolor}DC/WildStrawberry{0 0.96 0.39 0 setcmykcolor}DC /Salmon{0 0.53 0.38 0 setcmykcolor}DC/CarnationPink{0 0.63 0 0 setcmykcolor}DC/Magenta{0 1 0 0 setcmykcolor}DC/VioletRed{0 0.81 0 0 setcmykcolor}DC/Rhodamine{0 0.82 0 0 setcmykcolor}DC/Mulberry{0.34 0.90 0 0.02 setcmykcolor}DC/RedViolet{0.07 0.90 0 0.34 setcmykcolor}DC /Fuchsia{0.47 0.91 0 0.08 setcmykcolor}DC/Lavender{0 0.48 0 0 setcmykcolor}DC/Thistle{0.12 0.59 0 0 setcmykcolor}DC/Orchid{0.32 0.64 0 0 setcmykcolor}DC/DarkOrchid{0.40 0.80 0.20 0 setcmykcolor}DC/Purple{ 0.45 0.86 0 0 setcmykcolor}DC/Plum{0.50 1 0 0 setcmykcolor}DC/Violet{ 0.79 0.88 0 0 setcmykcolor}DC/RoyalPurple{0.75 0.90 0 0 setcmykcolor}DC /BlueViolet{0.86 0.91 0 0.04 setcmykcolor}DC/Periwinkle{0.57 0.55 0 0 setcmykcolor}DC/CadetBlue{0.62 0.57 0.23 0 setcmykcolor}DC /CornflowerBlue{0.65 0.13 0 0 setcmykcolor}DC/MidnightBlue{0.98 0.13 0 0.43 setcmykcolor}DC/NavyBlue{0.94 0.54 0 0 setcmykcolor}DC/RoyalBlue{1 0.50 0 0 setcmykcolor}DC/Blue{1 1 0 0 setcmykcolor}DC/Cerulean{0.94 0.11 0 0 setcmykcolor}DC/Cyan{1 0 0 0 setcmykcolor}DC/ProcessBlue{0.96 0 0 0 setcmykcolor}DC/SkyBlue{0.62 0 0.12 0 setcmykcolor}DC/Turquoise{0.85 0 0.20 0 setcmykcolor}DC/TealBlue{0.86 0 0.34 0.02 setcmykcolor}DC /Aquamarine{0.82 0 0.30 0 setcmykcolor}DC/BlueGreen{0.85 0 0.33 0 setcmykcolor}DC/Emerald{1 0 0.50 0 setcmykcolor}DC/JungleGreen{0.99 0 0.52 0 setcmykcolor}DC/SeaGreen{0.69 0 0.50 0 setcmykcolor}DC/Green{1 0 1 0 setcmykcolor}DC/ForestGreen{0.91 0 0.88 0.12 setcmykcolor}DC /PineGreen{0.92 0 0.59 0.25 setcmykcolor}DC/LimeGreen{0.50 0 1 0 setcmykcolor}DC/YellowGreen{0.44 0 0.74 0 setcmykcolor}DC/SpringGreen{ 0.26 0 0.76 0 setcmykcolor}DC/OliveGreen{0.64 0 0.95 0.40 setcmykcolor} DC/RawSienna{0 0.72 1 0.45 setcmykcolor}DC/Sepia{0 0.83 1 0.70 setcmykcolor}DC/Brown{0 0.81 1 0.60 setcmykcolor}DC/Tan{0.14 0.42 0.56 0 setcmykcolor}DC/Gray{0 0 0 0.50 setcmykcolor}DC/Black{0 0 0 1 setcmykcolor}DC/White{0 0 0 0 setcmykcolor}DC end %%EndProcSet %%BeginFont: CMR17 %!PS-AdobeFont-1.1: CMR17 1.0 %%CreationDate: 1991 Aug 20 16:38:24 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR17) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR17 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 1 /Delta put dup 10 /Omega put dup 12 /fi put dup 69 /E put dup 97 /a put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 105 /i put dup 108 /l put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 120 /x put readonly def /FontBBox{-33 -250 945 749}readonly def /UniqueID 5000795 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5F075EA0A10A15B0ED05D5039DA41B32B16E95 A3CE9725A429B35BAD796912FC328E3A28F96FCADA20A598E247755E7E7FF801 BDB00E9B9B086BDBE6EDCF841A3EAFC6F5284FED3C634085BA4EE0FC6A026E96 96D55575481B007BF93CA452EE3F71D83FAAB3D9DEDD2A8F96C5840EAE5BE5DC 9322E81DFF5E250DEB386E12A49FC9FBF9B4C25C3283F3CEA74B8278A1B09DA7 E9AE4FBAAF23EDF5A3E07D39385D521547C3AAAB8EB70549756EBA8EF445AF4A 497CA924ACCC3DD5456F8E2C7E36946A5BF14E2E959895F7C94F49137256BE46 4A238684D52792234869EAE1A6D8ADF4E138B79472D2A90A6CA99E2394CC20CD 3841733046175B20CEBE372327BF13428EED6A3E2FDF84C2DBA4B0AD584EE9DF B51828D3B8F385846158C29C9AC3496CB9692DD10219697B2ED4D425C3957FD8 C4600D76E045C561216EF05D38177243C314877A69A1C22E3BEC611A2EE5A216 9B7C264CF6D1839DBBD78A40610F2C0D7C2FE09FFA9822FF55035AD52546970F 83EED2D30EABB1F303091EBC11A5379B12BB3F405E371519A53EA9D66174ED25 A2E55463EC71A97BE4C04B39E68112956117C8252DB6FB14AB64534B4BCD568B 246DB833982B38CDE7268BBF74B6B0C18091E1B1F87D32D66F4DD023D1F10D2A 7736A960F72AC01F733A11023832CD68FB6288A5977743F781214D8FA9C0C3F7 80001321D4397771F728FD9EE57CFE7D9192B887EC883EB1505068261DC40089 7B7D2820F06515CD74513521F6397FEAB3AD3572D9A8269430E407E357422461 1785FC2782047F4C0339D79B16862D939F3A37F78E4E2174E4FBF132539CB760 207999FF86F6A3EBE48EB0A1CA635450FDEEF79EB16D853F3BF4B7A887B6794E 6C09C4B9C00804F4A8EF339D38F96F9967F3A7144D58344AFFF61EDE187221D8 B51DCDF9EC9365807657779D6B87E02EEF8ECE8A9B19BD81F4241E514F9598A1 F07A8009F1433A15DE7C3B8C947A729FAD399CF3063A4559D8FF924AA2D68EBD 828219B6DFD67093EF5F9E746FDFA8CAEC8C3234C27B16408CB7F1675159D3FF 5AA86E5CECB84445D4E673E22CE4D024833C563FC07ADFF8FA726CF08617BB24 0058A43072043A602AFBB94C2C184708A6C9FB95D88B9D3427FA1CC4E60ACE7B E530E21BD970723EF79800A4D39006CD068A9A333424C4B986A421C871818C4A 74F813E599B964691C5F40A6186B1B63C13DE92189AE6FD31334DB218952C8D8 6284E41AF6289D0F2D8F879DECB3F6A6E3E74F74356568618FADD03AABEC44F6 9C74FA9E8BDB9F044BEBBD0E4FFBAA6DFEB9C9DD9BC595CA53E5407B0E55DEFF 6382B3262C1C621CBBE227998F330E72EBA41CCE18DFDC99AAF89002ADA2A0F1 C3D376B1343825D4740115666746F8E0824830BF24207E5D456F115D435D96A1 1732EDB8F3F4E4C98C4DD12712B7AEFD95CB6AA113ECC54A92DA8FF222026913 B01AFDB210B1CB44F67B6134CB2C80DC1BD7CF41383B58C8DCF8E821BDDF7A2D 5E25CB69305E80FE805D006101147D533E2996D1DE9388AF0D9A89B6E99804B9 7B220522634B3EAE16E7B78B9F33B5DCEFA417A9A8BD7EA3DBD8CCC005207B71 731FA6679B21B09F06AF81DCEB3961866470679D84CB63D05E17286F2F8742E0 3703F05C707762434BD83FC6E3B87936460D308F83A0FECBDA6E77D3C4680271 DFAC7C568BA0293F49590B13B110DFC8A042409F5E1CCFCEB7F24801F9179B37 E572A13A6C72E0FBD3D3972B0A4588420CCBA7D9A4A055093285D52838AF4780 1743F0C89804D042C1C21AC0E9678CABE8541885B774B86C80395AA9ACD4B6D6 00917052E4CFB0AFFB51E6B81541549E4CDF43E53793AA7F46C0FC56B52A254F 0C48F2CF9BB381277A8AB5EA376CD19D65DC91BF8842DF986E24C7CAC41F3B02 2E3FB00822FDE9BA96B0B72D1EC8F74DC925DE1EB607E031368D77B879056D8D DB724A472EE6DD51756570DE44E9D1629E46B75C5AE786C4BF4F2046FDFD291A 3F595706201D536C683EB99935421754A205D20D017EF29F84703EDDB2786C0D 95B8199616F838CC22C7968A3D3A528B59EFF81640975D0F35DE67B65635A743 872B91A9AE9F321F6E15F0B8D496C5D859AF5CB0661447580374234A93A1E9F6 9C6486DC1092048EB11ED4F0D3BDA15F02E409AE8789008297BD09D38D1F32E0 A14C3DD4E894900B6D641D5D7C881A49A27AB0FBF6D4DD531A0B854920A9D69F EF6C7D611DE67BD0FCE948D3799A10BA9B892699C111D49A1955AEBD304CA110 04152A7FF822BA5CEAB4162D16A29B488AF1B7AFBE34BE46D376AA237AE3F29A 712CCE4BA6C7436356CF55E3A94D56441783C55D08051BC0A484B81F192A275F 46BD91BD8B52EC4930A56D61486B17322D38FF758D9A87F8F2BD42946F591DED 223BB09A2D7AD5863AB5B946AC2186F23D98750B20136AB330FED8D12D1250D0 33CFABEFCB67078354512DF31AC254063488C8AD37F2187C6496C418428ECA2D 4A96DB305EB1BCA094D206EE5AF3482F0D56684D6EFE2F1D6054578A9B530170 62D92A3D472D2FD86F3297A05B4020E2185178BAC73035307AFCD1B78BFE1AC1 215E4CE2140B75E2BC039A3121168F0813071C729FC0BF505B2AFACE98221D33 43D90EAE7F36F1B26113D0AAA1F7B5F019BA3693F09E4CC39E6ADD9390D491FE 88988DE0F36B688ABB1CD16DB0681DF34041B25062C9F913A058FA09E75CA7F7 B74A5D305033A59B14861EB474DCDFD69BBE29DB302AB26C2F325984A4448BA4 99A79E7D57FC08BA5C6586D7AE72C4CF1176CF62C138F8EAFFC6FEEA6D494FEC BAA2164B7EE55D385026D61F1187348E703288679E1E29AF0AF392FC48DD37B9 12ADFB7E66D83CC0994FA0E5C5E64A2FFDF942AAE38EBE9CBEEB01E35E3E8CC6 D76C1994D705775C7318E99EF96306D2EBBB731F29E49A07424AE68900C8F86B E93DE55418F8DD236F7CA01BCB7ACCE3339DBF48BF51A95E4F18D7F8FA5CC458 0FB7CE7A910F28EA3B2EF3C242C65AD07822C2E264F7F7C99562A0B3E2EF3B8C D2FC76F9EF034C49A5F2126CAFEB58751DC9219766CAFB2861FC382502B2601A 10B5B80CCECFF5559EABB8D38AF15460C5998F0EAB2CA96457FA3CBDA5C37229 241194AB84E421C92A16BDF61D3E631B377F02DE3C87812F92CD264A0DA3B9B6 0A50557AF8830CEAD1D26F013165525E1D6A2A7E5F524E0BCD1F89B763DAEFC6 C6AE7C625DFFA608DF05FE0D1382F9494CFB18308F4A766A451D460ECFFFDC4E DCF50165BF463A423F67D2F702EE71601871C6463E7F7DCA06B5201FB8E26A97 FB25408F9397CE981C31064FE0653A0E0350412B9CBE2CCE6DC6D6E1F8E06D28 9FA14B70B2271CBCEC665EE999DD0E56A3579509AA341E3C176C1A7BE91912A9 158C93A3B8426450AC4D8E4BBAAB1EBFE03ADC68CBEEAD20FC38A8E0DB5BA05A BFB15A78A3836A9D1009D5C7194F3AA0199EEFD0702B541B5361F85A7EFDA9BC 9F4CD080A7FAD53619CDDB14DDD4BEAB06AA3C735DF873CB992BA40E267D60F8 F2A7192354BEEC985B06DDAD6F3B48DE4D1D95C83FED892D84DEA0327473771A 9FA6CECD4766587D14D4F57CF806B9A507D765E37FCB6B6487CFB26FEEA113B0 BABC69D939D5F19C2A4E147D0FA1FC77278AD70A043A13688400D7B92B0A591A FDF2ED8BD2A35FF8FED364F47D7C6D217CDDC0EBC0D3A275A5A6C5B1B4A8FF06 5D53D51B6AC6A377A9735E6FE08025254C89136AD8FFA0E1D3C11CD0F4DAEED3 AACBE25A5CE9934DCC79D30A5D4C83C2DFA63447D36FBAEEDBEB55FE60F63122 8C1B38A50E271A132628D4DACBECAFB5856CED2ECA6310B71BC0B8B34CDF859D D73251D41A2B776A156EF7B29CA65ABD54CE5D298407CD658B19F98A2F56CF96 E438E12B6B378F0BBA379A5AD5A69BE90597D50416A0C13D4C743C578CCA930A 81B0182FED1BD7F7AB55888806552DE8099E3C14D2F61727A5705A2AECEC8F0F F36536996CCB4E1CB18C5B564A0483518FC50F8DECD8E679EA99876A3D8322F6 9A44AF6921AC50BAB5CE7CA63B468FA07A80F8C46443B47725B0064CE685ECD3 BDE666039634A9B508BE426ACE7B51F427863D71C7710F9AE8BF63379163AB68 EA1EBA583B754577C927F916145417F4CC49243FEE95222A91765F05D9245FF6 1C78E725D904D4AF98CE7A695E2503AECE8551D479EE5B3339BB8F2EEF05BE40 B391BD641B050167A99EFD46D0DF6BC73CD51F2F1561541649A8FFFBA23A4A55 652DA5E26835D826704DB03D60F29036BCD40F464DF78024C49310A80E72FD34 69749B7A3F1DB0B9DFE0138F00364885DCE3679C04DD0F80A2288DF066BACC6F 686CF9A3575A21A45CA63A76345BE894ED2832D8A943295AB0938A0553CEC4AF 40313E807AEBCB73EB696D2FB76156519E1EE1D832F689B64757765AC5C2E950 3FC2020E06A978D38002C041A0E2D6799D01A8D0ADDFA991D9829009F77A53EA 195D3C2CB8D45EAA10EC97BD8FF3007000CCC86B974710798A832C4E874CFCE8 B56F194F8A8E163951DC263D544F93CBF6D52C9E5F47BDB322F25E28A50BF167 184C8016A24074CD4124C8D7D7C40A45AC9B3E77ADD26AB3BABC5E4712DCB15E D330AD207F4EB94C2F87A57D5BCA5DD47AD26DAE53C5EE5E781EC0B162024F45 1F35006DABA3D2CD39ECD7CAA416EA2E7E44D8D6BB5F028AED55A155F6A283B0 2A5B205F7543052F8C7902715C4F418D709C22FD35CD1017C99B3B3651126586 D40C01A6E06FE05683A8272E09F6FA9B8C18AF0DD04E1F8F47B54DF8B69785FE CFA0FB6F6026AC49A1895BA27C8A3E4CD868B08C368778BE2EC3EB349B703EC4 0F51A9AF9D117EF8634456DC4142DB643A1FE52FE2C5C38BD7AB60B768742554 9BA6B3DF9E279DC9EB71F6F8C6C474F45E0E4955564A5435C9126019885F867A C6C4C66F223E97359F6172C7ACBAE7ABC01A76D52B50935C44618D89155F56F6 641B0BD6E21F80EBEC5547A3C19565D257BD5C5D86259E22C126F71ED8167B3F C47753500B983FFF9612BD9F37C15D386E76B16759F8CE187439C555A25999CE D6A7D3794DD51ED3F8673F80DD5E4EE71040F899672DDD2DCA898D043E9B4263 BB11D5974BEBC0235A9385B7E251D877A25DFB33EA09AF4BB71D9094178E16C7 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI12 %!PS-AdobeFont-1.1: CMMI12 1.100 %%CreationDate: 1996 Jul 27 08:57:55 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 13 /gamma put dup 66 /B put dup 77 /M put dup 97 /a put dup 98 /b put dup 108 /l put dup 109 /m put dup 114 /r put dup 120 /x put readonly def /FontBBox{-30 -250 1026 750}readonly def /UniqueID 5087386 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMBX7 %!PS-AdobeFont-1.1: CMBX7 1.0 %%CreationDate: 1991 Aug 20 16:35:49 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 101 /e put readonly def /FontBBox{-55 -250 1289 751}readonly def /UniqueID 5000765 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5F0364CD5660F74BEE96790DE35AFA90CCF712 B1805DA88AE375A04F3C90C160DE16F890E93B13B46BB2F4971D900BB550E53F EC6248832A83CF441B4851445885479839AFAA2903A27676E5FDBCD653467C5B 6757DA1B722133018873A10B4FD9D710BBD9BE518D989B67DD4533F8702D640E B84C3CC2607748FBD7C4BC6DA98537C7A83BCDCD871BC342E318F22902994EA5 8F5F698960BF55B6DD1ADBAA57D96E80D7C28E06447C5E0131B450234C39D332 D6EBE6E76DD503B658866DF4DB6774597338B1DB90AC6C0ABAEBA29CE9656E89 167D88958F3BF262133689AD41A5B9A90DF2838A221C5067B73066612A0FAD18 6A3670B2A69D1731367C8335600294ABC365F383F983A8AB1E37C1C1804893F7 DBF122DA9C3843D1715ACBEF92F28AECE850981251D1D25F13B0DE4320D26157 D14147622A29E7E7F6A037AF34A0197D57AB2A9F7129001F7F636F3B07E0F12F D409D880B878EC8C911E3B1F24AE299AC56227FB9D6ECDDDC5F8DFCD18D8D0B1 4BF4C36A2E36F69E7291A1A0F738ED27D586BAAE8C04E00D5B3C88316AD3374C 5164218F5588EEDBF966055C55E9781D75B1D7B9C1A2FD2682E7CB88FA9C6889 8C5510BD1964BB505CABF99F91C7110745DFBC4B8A2A15295320EAF27A97ED84 C6E59474C2832859A5E2536E33893D90929D6D2585C73A6F3D316B96DCF60413 912E288DC3945E3A2C53EE1580FA68D40CC336D9AF2EDB87DAC04ACBF223D379 5482F7EF56A8DE5175D4D988BD67040B7B4634B145F6C995009C1D9671217E37 758B75D54A26EF8D6F56822318B256B2C43B27E2892E250E98F438334182171D 99CF39FD8F18FECC0C511B82F9E4B4F4105FB790D635D44CC9EADB5CB62797B7 1804D607C2DC0FA6B8FA3189DF2279502B210274CB58795B479224606D2AA9A6 05D685D9B8AE0A4E1BF5FF1D53B731F867DA6707E9EC1C52FDCA85250DFB837C 9D349CBD71D74C41F9291707C354362710D75B78B36BD6ADF9A96B118DBABC6F 332581993C60493C55B3AA7437CF906E0E29A98A6A0306087169CC7176C078C9 CBEEDD8CDDD0DAE0746B546DA45BD6A14DEA27FB846004144DDFA4C50B23BA5F A0FD00C465A0F6655660C1409C75C8A1DBBF135E3D97A94F8B20D32C4486310C A9B200EC42E73E7F7FDC206D511C9D6C07AFA946D916AD75E5E50F1D51BB80C3 804E6F163C739C3E506DE8457216DEA53B49316D888DB1E0D2859291A26D1A35 F290CB277C02DEB8AEDF62F3577E7FA679948944B9F7F70F0A9FA699B210C01E B30D44093968E2936A 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR12 %!PS-AdobeFont-1.1: CMR12 1.0 %%CreationDate: 1991 Aug 20 16:38:05 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 19 /acute put dup 39 /quoteright put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 54 /six put dup 65 /A put dup 67 /C put dup 70 /F put dup 73 /I put dup 74 /J put dup 76 /L put dup 77 /M put dup 78 /N put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 89 /Y put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 103 /g put dup 105 /i put dup 107 /k put dup 108 /l put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 121 /y put readonly def /FontBBox{-34 -251 988 750}readonly def /UniqueID 5000794 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY10 %!PS-AdobeFont-1.1: CMSY10 1.0 %%CreationDate: 1991 Aug 15 07:20:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 1 /periodcentered put dup 2 /multiply put dup 6 /plusminus put dup 10 /circlemultiply put dup 15 /bullet put dup 17 /equivalence put dup 20 /lessequal put dup 21 /greaterequal put dup 23 /followsequal put dup 24 /similar put dup 26 /propersubset put dup 27 /propersuperset put dup 28 /lessmuch put dup 33 /arrowright put dup 36 /arrowboth put dup 38 /arrowsoutheast put dup 49 /infinity put dup 50 /element put dup 54 /negationslash put dup 56 /universal put dup 57 /existential put dup 59 /emptyset put dup 65 /A put dup 67 /C put dup 69 /E put dup 72 /H put dup 82 /R put dup 83 /S put dup 87 /W put dup 91 /union put dup 92 /intersection put dup 94 /logicaland put dup 102 /braceleft put dup 103 /braceright put dup 104 /angbracketleft put dup 105 /angbracketright put dup 106 /bar put dup 107 /bardbl put dup 110 /backslash put dup 113 /coproduct put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueID 5000820 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: MSAM10 %!PS-AdobeFont-1.1: MSAM10 2.1 %%CreationDate: 1993 Sep 17 09:05:00 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSAM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSAM10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 98 /subsetdbl put readonly def /FontBBox{8 -463 1331 1003}readonly def /UniqueID 5031981 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSL10 %!PS-AdobeFont-1.1: CMSL10 1.0 %%CreationDate: 1991 Aug 20 16:40:20 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSL10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -9.46 def /isFixedPitch false def end readonly def /FontName /CMSL10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 44 /comma put dup 70 /F put dup 97 /a put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 108 /l put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 120 /x put dup 121 /y put readonly def /FontBBox{-62 -250 1123 750}readonly def /UniqueID 5000798 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D5993DFC0930297866E1CD0A319B6B1FD958 9429B9D40924DC059325D9D4CC0344F3F997A99E6CC0676735EBCD685AAC9142 08DAFEC78BB41AFC2F1C219910BDF41D6279284EF600B69776CA15BC8A34347C 30783C52AFA60FBE3E353E2AE354CF87B558776A22C776C7A0B5AB5CE1F941EF C2D9CAC37294BF407A671F10E4743BF842143F4F7DFEE643BA3BBD8BB9E3F24A BCCF7F0ADF8BA500620C81033EAE8C4EF2C1DEF13AC575F1B3BBB66F093D3B78 5412B82B67FFA087AF57182B2230F9F2137180CA58A7D9B2C822FF04BE6CD01D 43B2CA7058C7B953F6D9B5D6E91ECBAA5CDE1159B0E59C83DBAD96D6C8C8BAB1 374EF652D10C0F3EE7104472C98DD3572AAF2D45A70BF7061447E21EE3C3BF23 DF39C2D1B35B42CD5297BEBE6BC94F7C9DC6E61EC67E4F677256FED9064BD3E4 B51A71B1D27CA4E5AA9E1D8080E6DAB5310711EEF87C40859FA935B19524AE83 63B163FA8397BDFF443227FEDF7DB27DC35D89FB1C5E435DA0619A5C88AFC73B 89A2DF5E767C5B536BC7167A840A0C32BD57A14DE69A7D0D819AC36FF32F908A 5070F32983BB007437E3500799DF5E0AD3710A4C0000F0098D5BE99F2EB9C1C2 C444FD9552D0DCA098A94B3BF176F511CEE13DB7EFFAED7C47B5ADCF8D4700F5 7B6DF50EE617C00966B9A2828882804DB7477F4A8CF5345B7F3568B4F72BCE73 2E2AA5BC4B4C70E21F3AD9AFC3B8605A00D67EF9ED1F4D13DDAA920D45B43CE0 0941BF17CF05D2B777C11D4D844AB20C0693D1DDF00B27D9E1AA2D98A4A06CC6 D342AD8F644F4787B66CA7D861E7CE13FCDA85C1B0C9F94009768EA89838EBA2 7818F40BE8C5109DE131D14D65A0A8D501A75EBAB866ED803A9D26E70101BF80 60AEC9861CB1E348A19FBB5E8C6CA5C458F7845025BC62471711C68E62DD1889 51AF98A786F7921C2EFEBA0B29C5DF0F138487C3586E2D75B48D67CA8750313A 2319CC656058052ACDB3212FF310A84E03FC883B282964D06897187A7FF7F948 F3652D513958D24337B1F37F871DC126E25A8ADE1C2F1E411779D7C4F10B0496 FBAC9F7C51E96F012049FD993A6D65D6EA45625E11346DE806B9990B629AEE31 B347C7EAC0775C64BC28B05A4FD5C00B31B3025E8FEDDEDEC649616DD2AF72FE EDEE901516D782C2A49DA1AACDD40F6D1387601AD011AF0BD7D6CD195E97AB64 AF58144B226D1BA58D4ED62468A76EB9F50B07650B6D99E43D7418C72D2648E5 DF76F661958B8C069850136A42645BA44B3FBD51E0F5BDCCFA5D511C8FD9B80D 6A1D2BACD7DE605C8C9E996D7A404A29979D76703FC6E4A3C90B9439F1D23B26 E347475B1E46471D38747507F5B8E93AB9AAEED8FE187841FCFC9219FDD37DA8 AB06590B0BC158DB14FFEB0C41C7C0B7642F8B70D7C4603F79E44FC551887A7B ED7ECB34109AB21604A6C1193C3FC56649789F4C3693DD0DF5C283D6BB0D3673 0A492D76AD3DE7C521C892981148CCE305DACA9C978A549F30FACA579481197D 39324A33FDED3A1B9D7C454642594D4E140C28A5F06C4D13832C143AE8A67F14 2AC7516492BF4482E3F984DB23A18F684828392E7351502FB0A462EE4CF423D3 074D8173E7A0ED74972C54F79EF4AF2E3669BF84CDAFCC2415858E4DBC47DE0E 6B64AC58C61CA56D31575AFF17E2DEBA961AB4C2851091148A5E86FEE189EBC6 3583C0C13B11817CEEBED54E0A9D7C01F582460359923B46D9E681C6E7BF94BF C8B226C41B59799369CF0D85E4F9F43A90499DD000889C6F7D9BD97B7B75A8C9 EE2D275A4D5697FAC0FE876617B890F1A5977DBB1059DA5E9FC150F9A1BA1E74 37F7DCE0720B7AC52C057A2FE8255841F31010600470DBCC2329FD48A4509DC5 DE8284866B2E80CAFB335A32EF6F61CB38A0129C086D79EF2823D407DAFDCEB7 9C74D7DE790A563AEC18DFEB0B3013B21F676D1B844C3723D558A205A5D5A424 1BBBB5F1B320AB91C419C8F71D33EA22747CF50A702C3EBD0D5EE93BE68F0579 7CE78165BB1D9605008C22E9F91566075C99869D1D9527DB13DC8BA4F188AF00 0DFF0BFC5A9D6D4F6DD6361712F24C9786CDCEDCFC719B12252EB5A7158F9793 DBAF8817D19ACCC6455C3664A69F7AA7E56085BDC77224CC76CC429CD79C2CC3 67936937BF85FDD72B78E5008CDE73B2803548E8834D0ED8D667AE171C3718DA BCBD005B18025C521C1585306B10C6C1C459CB26A242946F16FC043D3DB58A1E E88F18E1838F6BE5089C11F9383D30FB3B8D49AA6E4D8CF0178736D16694863C 7D45ECFE4AE174F1F31F0E7E0C468BEA9844790314858074D5A22AF9D8EDE2A2 3E6A89E8970BA004B258524D9B7FEE21BA984BF6F2A501A1B5C47B0DCB841794 69A7C6949518876CF7344575642708D83981570A488889BEE85DB5EECFA8625A 7B50FCA6AF3572972EA4A51DDC47DC3A8F56287D755F764E0A5E59FA3F679C04 E035740EB844ADF92E84366810979F1DEB30B4380DE35AC5AB205D90D6C57B6D 4D824E9175BF57D5262C62E8C12FF366565E78BCA4E707546142C48966E44F27 722F787B77CA2343573D2C7C711710AEFBC1AB01AE59C62AEEB47A7A449979EC 73D2E0D8F4E9868937F858C4E74AF9DB4742F1EA8F0F3DC3904A5DA245A2F8B2 A982CD3058D85DC519577E669BD76F4BA7952DA1C913ABB6363C0607F36AF685 C4EF82DE90DBE2F821E93FDDB73AC3D1EDECA68063ED707E02E8D003CC89C44A D5415E825468A9AF98F4981C2D0A7DC1A92807F9CAF92535237C6AA9A8E40046 151EDFAD1F7D83D81D5363756EA8D75993DFCB74358E386E6D6EFC1F93F0041A 2A40978795F264FD5912590EEF0B982768B72027FEEA61DF7B14FD11C0873436 F1B526DDE7F4DEBB435220ED3AA52833CD1ACF845CC29BBD8B8DE727E85088EE 1FF755D5D9175DE78202C078EB0919D61B647E5CCB45BEFC9081A1DA8F3D166D A4E6740ABCB3E7A0EF47532E1718E7E9FEC7EBC444E544DED1F51FD42E4F899E 6E416E00C30ECF56815384CB15F6B9C6863C740943BD1AD924FB8A1D7D0E2316 08C8F514E44EE63CC7FD025DDA5D28493E6CC1777064949688509552422200AF 4E9F874DD0DCE7A11B1BF1EA79E7261663B99A7A1852A387FA135101EC3D5DC9 BB2879233A0D9E1DA9AB9981D31182D24AD175B6BE61B76E77607672B174BFE8 0F52C3A0943C05C97D62916E2434D7E54E33BB5C5B0755275D006571960B388B DE96E79DEA3C4CF19683CF29B56157D37EDDD3735A00ECB633DB96E8DC1BED27 B328F38A9E50B758EEBC6F9941692F64FF681D2B23F9AB36C904AD4232035149 3C2A3464E4432E4C4C6136D98D580B8941313D60D6E65B3F9314E3F160CA2B62 4403E6A023605E7021FA33624D18F7E11F02E09637F77F148B18CE2A93B482C8 1CC63A1621C3B8CB8273EC7524AFB2CB426B843F6D237A9B07B26B860822529C F148D463307A6C4B3AC625E39871E0857ECACAC892C03A29EDFDBDB532B8A1CA 9BEB75A73488BE0EA63E7821A8EF3D4C19652589FAE2DF6EF7439A0BC3D99C52 2D23EC4AEAD5BCA41B46D9D87832FFBD91B8FED02D05AFDCF2C50812C4557163 F1D15719D6B12F703D08929DB1AE4941256B6621F546592B932D159D87D31822 9E20A33BF960AD5212A48EB7D34FAB0C7A745521303A821DA8BB275E340D05C3 386E0D4E0D6F7D37C671D8F8C6FD9EC15AA9F02C45EC3E34A378778CA0BDA265 48D73FA054B461E94DD1ADFB3AD0047296C3B7E92253507E0B4DCB16951A6EFC F70830CCB6CAF2A0A5DC787EE9164F4DF427E3015D495F154F5C419EF06B54AB C59B51FF50AA66EA8A3C85F0212357BF9352BB99DC2E0A123491ABBD624A9435 D37E5DD3BD6EA09FB8082943EED8EA2FAEA9BD325979DA23DC82E49DF1A4D89E 9F7D9B192CEA291763662E2B843A9536AD87DBDCB4A58D76031122EDF4BE410F 05DAFF763D4B541E997E3F4042F6519CAA88E8A6E4D26FA48E1996A270F508CD 140FDABFA0B136AE08E920D8E449346A6F7D8D9FA48D6BD79F2929168EE3739A 383698ED629930145D2A12D32FC9FFC9EA7FC87F8332960140AB04ECB9C56639 753BB7D2410F675A026456EF3593EEF8AB02E774C03C11FBE21F3AF8C2878FFB 2F42CFC78F8A9AA3889EBADC593722615785E19F6A00E01B45694F6102E3E599 2783CF2DDA5287D07EDE2417E123F9AE5244E69866532EC8FDF7B741F6F472FC AF3960C2320A2AEB969336792C7FF87CB61EEE094B75E9417E7C4077A7C04BED D47E92DC901A02A2CCB7253ACC932CF589CCF099A32B2385CE299A53900E2E04 CA78EC6BEBE3726A6F8DF244DE719C587B0E3AC7FC5B4B5D808481B0DCDC0441 1F96FFF3F936873A1AE65DBCB9C1B83FEF483FE4C8F2AC04266F5A2C0F231D5D 38B7F1F35F8DBE7AA2509B184DA40D7478A7A7C83F636376DA6A16FD3A98FB80 95B17E92170071E68AB3D46AFC0AD15E6152D63DCD6F9694A572597386873A17 E3194A2FE4A3D53B002EC92022C09EA9F00D7F198FEA65B8BBAA2C2C35FB39CB 3797165D78CC7EA9BEB0F7A3E35ECEDF95583A8FE6EB837BDD256BB18427BF4C 99CD6D4940C536DF6887212116D7D59E4AD74E845ABAF0BF5A577D0E8BFFF4EE EB21AE5DCB4500ECED41D23CF006FF2B430063422830F41B715B5D333A60AF46 10F8F1218399B3B80DC86556BF07D4C8F826B8B22E71BDDB30B853EA70747F17 9E0CE663D231FCE9C01B44338E2B8569F2452FC05F061519F1038028275D60C2 83EB4051872C76BB464BD9181C0BE29A681B3A36D779568613EFC7FEEFA81163 FAD35E3C3C9076AA30E2E43B8D3AAE11421CE6C6A4456443D4F5DCA6326BFD29 8888FC57539932417DADF9FCE1FCEC91556AAFF0ACCC3654072EC8C677536CBA 05D2E27B76D2E89959DCF054B0FA2C42EC171AE796BB562E8BA0EE1A9CC18286 49A2729FB175EC01629C685FE71B655589D330D965321D51B605B76071E57370 F73C7A5A8E27FEF576155A4DD80F2F33D4F9DCF4CEF7A4798A28E2C0B2D91FF2 ECE77327E457B2BB8B6C7A3E8777BE5968835C7897E9987A088674CE75B3807C 440EB9C45130A71464963942DEC791D510ACE9C925A0AC03CD5AC880C9DB6FF8 32776555D47008A7AA48FA6CF991D1F4CEFFEC5F8E363D92C1DBFCEEDAA62F77 1558F8A7222C79AA18489AEC39147CE10263BF55C4CFA439835AD67927B8FC48 B6B58DD4BFDB7371DDD172A967DBCC0ABD9975053B8C504EEFAE0A3138F50394 EA4C9633087298F19A0B15CBC109B23F5A5017AF6FC521DF4D3F95385085C951 601E286CF88D1E532242262F03316999111BC3EC7BF50CF9F08E63B05586B8CF 2F440F8CFCB799279CEEA9687FFB1362E10D865C5D74138D05372D0A1353059D B3544011FCA60814444C8DCD5359A2BFB76D6EA34B71C840091FDA545F99E7DE 136EC7586DBCE2EB46927F5D5BE63FB10D62CA2DA239999C043AECE3C70CCBB7 F20F34F55727D5373A656FD7A9C9C3CD1F1E16633C32D840433AF4B7B067ABE0 54313139405B6A7BD2C16BB4BCF76051F19641CA375A0DFECA16EAC3E8F9549A 16D8721DAE7E872988B17FB66801C6710BFCC2D006CD44F42D6E2F9430A4F9BA 673A2BDD93B24E02091ACB0C8414A1C8C64766C41EE7E6CA117B6454212E2EBC 658EE256A34903EF01960AC11EC002CD15B7E03F2F991B52583699946C2FD434 CBAA305BCDA0280427EADC58918A90396FC220939F94FA58F8FE821DD77E4AD3 64E32E8EFFB4AF72B99AD7905671E35A731836C78322E1C2C100D32D84FAA813 856063B15FB3C11B5C1F7A2B2A544A9532F89BA7BE92D137A9823388A948BFA0 46EE2F133CF7182F4E07E5FD95C10313695EAA608F2D90146FFCCB48AD56E969 31E4457822FFCE50A6AD3EBEC8A8B180C56436E268AC44829AA4614E8801CA28 BCE09BEBB3D88BACBFF332DC1A02A7A46F0B4E2F6526B2D6E82E04A54AD2B989 C9FAE3E2D0CA28566878369955EFB1165D98444C0DABC80E746FAE6C05FC5587 F56E77FAEB14503328645CEBCA6DCFB882D29D35E353FBF772E5214435969ADC 200943EC3E4528EAEA3E32C42891E790612781DC0FD80CCFADEADB3EAB3D74B1 202F73BC7CE596F9F53D4E340A880B88F0831A8C4B853F663D9CE742F4FA0967 B1C6ACDBB27A62BE1AF5BF04769580E268D1C63C4D237D7DC3349E15B214958F A5F76700748CD478A7A3300E68CE1C5386A3E7144C76C12606507CEFFB30853C EF35923ACE051E95AB81538EC8BA6E46B33DE59D7CA6189433A38419DE8A0AE5 0F8D6E84536934B7B520B84D567CE97C5DB74DA63CF14F88F8D84CE8E0C88AF0 D266A4CE85C191916120A86943821E58D4C745A9280813A27CD2AF6865D317BC CA5CB5DB8DE39ED1DFCB000EEEFE887C81C2A2C904A37DB0 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: TeX-cmex7 %!PS-AdobeFont-1.0: TeX-cmex7 001.001 % Filtered by type1fix.pl 0.05 %%EndComments 13 dict dup begin /FontInfo 16 dict dup begin /Copyright (see\040copyright\040of\040original\040TeX\040font) def /FamilyName (TeX\040cmex7) def /FullName (TeX\040cmex7\040Regular) def /ItalicAngle 0 def /Notice (converted\040after\040April\0402001) def /UnderlinePosition -100 def /UnderlineThickness 50 def /Weight (Regular) def /isFixedPitch false def /version (001.001) def end readonly def /FontName /TeX-cmex7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 80 /P put dup 101 /e put readonly def /FontBBox {-14 -2954 1627 771} readonly def /UniqueID 4314415 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSS8 %!PS-AdobeFont-1.1: CMSS8 1.0 %%CreationDate: 1991 Aug 20 17:34:12 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSS8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMSS8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 86 /V put readonly def /FontBBox{-65 -250 1062 761}readonly def /UniqueID 5000801 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR5 %!PS-AdobeFont-1.1: CMR5 1.00B %%CreationDate: 1992 Feb 19 19:55:02 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 3 /Lambda put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 91 /bracketleft put dup 93 /bracketright put dup 99 /c put dup 105 /i put dup 115 /s put readonly def /FontBBox{-341 -250 1304 965}readonly def /UniqueID 5000788 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY5 %!PS-AdobeFont-1.1: CMSY5 1.0 %%CreationDate: 1991 Aug 15 07:21:16 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 3 /asteriskmath put dup 24 /similar put dup 48 /prime put dup 50 /element put dup 72 /H put dup 106 /bar put readonly def /FontBBox{21 -944 1448 791}readonly def /UniqueID 5000815 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMTI10 %!PS-AdobeFont-1.1: CMTI10 1.00B %%CreationDate: 1992 Feb 19 19:56:16 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 12 /fi put dup 40 /parenleft put dup 41 /parenright put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 53 /five put dup 57 /nine put dup 58 /colon put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 70 /F put dup 71 /G put dup 73 /I put dup 74 /J put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 87 /W put dup 91 /bracketleft put dup 93 /bracketright put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put readonly def /FontBBox{-163 -250 1146 969}readonly def /UniqueID 5000828 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMBX10 %!PS-AdobeFont-1.1: CMBX10 1.00B %%CreationDate: 1992 Feb 19 19:54:06 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 40 /parenleft put dup 41 /parenright put dup 44 /comma put dup 46 /period put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 57 /nine put dup 65 /A put dup 67 /C put dup 76 /L put dup 80 /P put dup 82 /R put dup 84 /T put dup 91 /bracketleft put dup 93 /bracketright put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 119 /w put dup 121 /y put readonly def /FontBBox{-301 -250 1164 946}readonly def /UniqueID 5000768 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: MSBM10 %!PS-AdobeFont-1.1: MSBM10 2.1 %%CreationDate: 1993 Sep 17 11:10:37 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSBM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSBM10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 69 /E put dup 78 /N put dup 80 /P put dup 82 /R put dup 83 /S put dup 90 /Z put readonly def /FontBBox{-55 -420 2343 920}readonly def /UniqueID 5031982 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSL8 %!PS-AdobeFont-1.1: CMSL8 1.0 %%CreationDate: 1991 Aug 20 16:41:02 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSL8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -9.46 def /isFixedPitch false def end readonly def /FontName /CMSL8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 12 /fi put dup 44 /comma put dup 48 /zero put dup 50 /two put dup 51 /three put dup 59 /semicolon put dup 69 /E put dup 74 /J put dup 97 /a put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 105 /i put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 120 /x put dup 121 /y put readonly def /FontBBox{-57 -250 1183 750}readonly def /UniqueID 5000796 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: MSBM7 %!PS-AdobeFont-1.1: MSBM7 2.1 %%CreationDate: 1992 Oct 17 08:30:50 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSBM7) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSBM7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 90 /Z put readonly def /FontBBox{0 -504 2615 1004}readonly def /UniqueID 5032014 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSS10 %!PS-AdobeFont-1.1: CMSS10 1.0 %%CreationDate: 1991 Aug 20 17:33:34 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSS10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMSS10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 67 /C put dup 85 /U put dup 86 /V put dup 87 /W put readonly def /FontBBox{-61 -250 999 759}readonly def /UniqueID 5000803 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF7158F1163BDCEEA888D07B439DBD4E8B4C9 D198C03874B5E6F8FBF4922065A92BC3E66D05DE53971CB1424510E892442858 D69CE1F76E4DA76C87C763A4B2FE36321E54B1328C9155B8ED6361855A151723 3386AEA3D042B8D89C8C0E9A33E5DF3B466F7BB8C2C8A4ED4CDAFF55FC6D3EE6 0AF2CEBFC1AC3A6E6692F8BB81F82D86BAE85016AD62FCB05467082C2E5AD348 44D1439C2B59F65590E57CA0DE481A7A34E79931B1513C4C30156170409A4BB8 46D412D1DAF88AD30722F12DBCA1CCC6B4BCC28D06B0D29149DDEC520C8FBA13 6B82E2E1790F00B216282FF122EF0D47B70A1B29514DDF7C0435ED238C14BDF5 6DA243117FBEF7398F97EB95597707ED63C6797EBA1B46EA19ABB1DABDA171B3 16CD500F5D64CBFBE4F9CBC3E66A34427D3C4D0C432710289381F9BFD91B4FF4 1E3A896C3EEA2F3105C218877D6C0C6B763760FA364D00065E1CAE9DCB5676ED 286A9ED0D1C946DCA6A2A670EE0936FB4706CC62E234CFEED34AA615C48D2872 A087F30990C85E64BA68F3D5C117123467DB411C9F2D6F6858CC70C1E352C477 713097321B4C4FD4C5CDE305415F998E7245908EEDE6E056A736EA77BD8C639C 3A79FFD0B74B3D28F0494A115F2841CF8A8827AB5608F96FD8998A5F40FB3DFE 3AA0C7696DE4E1D18DC0D6E84B943175FC38FFC42A9C0CBB13A908978C98BFE5 034F88480F32B9DEB2FD228FF6CB0B89B045AB02020C82E3F5716DC640613185 9F597CE262729BC52132F43922B9E28BB71A30AC8709634561B22D13C4FAFE0A 12C4451969226B220038AD8DDA990A4E2CAD53DBEAB698898BBD3046234EB4EA 901287E71CB41296C431383AB85F18882F65BE36923F6C0FD6FADCA2A89F1F1F CB8DAED682C67307EFB12EC751FE4A8BEA033D08D35F09EA030B8CD4DC52C82E 973D6C9DAB561CDAD2CF26F517D4D3A392D05D2E09F12127573427BA64140333 2F98EC1B1EAF5407FE6F9D338BC7695D1CDE823F4694F12D4E7AFB8D96B1A812 AB8243E9592853B4D560D0700AD6A74AA7508F534B6A8A31458323C953913F25 E7BB798B49AD057FB620301E773AD5423CC5E62928DF7EE2EE2E60F01F2102F6 C5FE99976BEEF589DEA4AE89E8F357C43E5079F9BE33FB4D4117B6647192A960 F57505454A2D3B1FE82DF3A414FBD6EBFE63737F3407B5BD7F7BE3A21F8A752C 4FA976315E3FA7E1A12F585FC2EC3A9E926EB3923F08762FBC3203D1F1DC9528 07B5C1F1F6A14A44F1732F82A8BAFB375B26BF1D776B6180BB71BB6826B343C4 93A94B40BC989FDB61952B48D0403C382D4E4D3FA1623029531FC61100DBF081 8748003781EE88B512B487579296A907EE536B5DEB73E064AD8028EB1B0D6135 4150384CDAFFBA66E4CCFD0337594F7DCB0E6B6752599BB05C2A6DA8EDAD1AC7 E2A21B1990FBDB911F21054815A778F33B9CD745527524973BF8F71C639F8FF0 F659992116D87E0938E287F6C04C4593CC92392E0FE514217BBBDD6F29D6647C B6B99C3C4F7F46B717915FC30BF98C9FB119695CFD8120D651D76F751DE03298 092694C5A9CAE4ADBCB7FD383A49A349A7CBCCF833A528F5E22D2D463FCF5EC5 F5FF4B6B6DAB716D47C14856BEF8C7F6F484D5C9D88997CA67EB40F793C590AA 024A5B818F53E22273D1DF7D8C083A4E1B4D5C337BABCFA48C 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI5 %!PS-AdobeFont-1.1: CMMI5 1.100 %%CreationDate: 1996 Aug 02 08:21:10 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 12 /beta put dup 15 /epsilon1 put dup 21 /lambda put dup 23 /nu put dup 29 /upsilon put dup 58 /period put dup 59 /comma put dup 61 /slash put dup 65 /A put dup 78 /N put dup 82 /R put dup 96 /lscript put dup 99 /c put dup 100 /d put dup 101 /e put dup 104 /h put dup 105 /i put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 114 /r put dup 116 /t put dup 120 /x put dup 121 /y put readonly def /FontBBox{37 -250 1349 750}readonly def /UniqueID 5087380 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY7 %!PS-AdobeFont-1.1: CMSY7 1.0 %%CreationDate: 1991 Aug 15 07:21:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 1 /periodcentered put dup 3 /asteriskmath put dup 6 /plusminus put dup 20 /lessequal put dup 21 /greaterequal put dup 24 /similar put dup 26 /propersubset put dup 33 /arrowright put dup 34 /arrowup put dup 36 /arrowboth put dup 38 /arrowsoutheast put dup 48 /prime put dup 49 /infinity put dup 50 /element put dup 52 /triangle put dup 54 /negationslash put dup 59 /emptyset put dup 65 /A put dup 67 /C put dup 69 /E put dup 72 /H put dup 82 /R put dup 83 /S put dup 91 /union put dup 92 /intersection put dup 102 /braceleft put dup 103 /braceright put dup 104 /angbracketleft put dup 105 /angbracketright put dup 106 /bar put dup 110 /backslash put readonly def /FontBBox{-15 -951 1252 782}readonly def /UniqueID 5000817 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMEX10 %!PS-AdobeFont-1.1: CMEX10 1.00 %%CreationDate: 1992 Jul 23 21:22:48 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMEX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMEX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /parenleftbig put dup 1 /parenrightbig put dup 8 /braceleftbig put dup 9 /bracerightbig put dup 12 /vextendsingle put dup 16 /parenleftBig put dup 17 /parenrightBig put dup 18 /parenleftbigg put dup 19 /parenrightbigg put dup 26 /braceleftbigg put dup 27 /bracerightbigg put dup 32 /parenleftBigg put dup 33 /parenrightBigg put dup 34 /bracketleftBigg put dup 35 /bracketrightBigg put dup 40 /braceleftBigg put dup 41 /bracerightBigg put dup 56 /bracelefttp put dup 57 /bracerighttp put dup 58 /braceleftbt put dup 59 /bracerightbt put dup 60 /braceleftmid put dup 61 /bracerightmid put dup 62 /braceex put dup 80 /summationtext put dup 81 /producttext put dup 83 /uniontext put dup 88 /summationdisplay put dup 89 /productdisplay put dup 90 /integraldisplay put dup 101 /tildewide put dup 110 /braceleftBig put dup 111 /bracerightBig put dup 112 /radicalbig put readonly def /FontBBox{-24 -2960 1454 772}readonly def /UniqueID 5000774 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR7 %!PS-AdobeFont-1.1: CMR7 1.0 %%CreationDate: 1991 Aug 20 16:39:21 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 1 /Delta put dup 3 /Lambda put dup 10 /Omega put dup 22 /macron put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 54 /six put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 61 /equal put dup 90 /Z put dup 91 /bracketleft put dup 93 /bracketright put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 103 /g put dup 105 /i put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 115 /s put dup 116 /t put dup 120 /x put readonly def /FontBBox{-27 -250 1122 750}readonly def /UniqueID 5000790 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI7 %!PS-AdobeFont-1.1: CMMI7 1.100 %%CreationDate: 1996 Jul 23 07:53:53 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 12 /beta put dup 13 /gamma put dup 15 /epsilon1 put dup 16 /zeta put dup 17 /eta put dup 20 /kappa put dup 21 /lambda put dup 23 /nu put dup 26 /rho put dup 27 /sigma put dup 28 /tau put dup 29 /upsilon put dup 34 /epsilon put dup 58 /period put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 62 /greater put dup 64 /partialdiff put dup 65 /A put dup 66 /B put dup 67 /C put dup 69 /E put dup 72 /H put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 82 /R put dup 88 /X put dup 96 /lscript put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{0 -250 1171 750}readonly def /UniqueID 5087382 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D77639DF1232A4D6233A9CAF69B151DFD33F C0962EAC6E3EBFB8AD256A3C654EAAF9A50C51BC6FA90B61B60401C235AFAB7B B078D20B4B8A6D7F0300CF694E6956FF9C29C84FCC5C9E8890AA56B1BC60E868 DA8488AC4435E6B5CE34EA88E904D5C978514D7E476BF8971D419363125D4811 4D886EDDDCDDA8A6B0FDA5CF0603EA9FA5D4393BEBB26E1AB11C2D74FFA6FEE3 FAFBC6F05B801C1C3276B11080F5023902B56593F3F6B1F37997038F36B9E3AB 76C2E97E1F492D27A8E99F3E947A47166D0D0D063E4E6A9B535DC9F1BED129C5 123775D5D68787A58C93009FD5DA55B19511B95168C83429BD2D878207C39770 012318EA7AA39900C97B9D3859E3D0B04750B8390BF1F1BC29DC22BCAD50ECC6 A3C633D0937A59E859E5185AF9F56704708D5F1C50F78F43DFAC43C4E7DC9413 44CEFE43279AFD3C167C942889A352F2FF806C2FF8B3EB4908D50778AA58CFFC 4D1B14597A06A994ED8414BBE8B26E74D49F6CF54176B7297CDA112A69518050 01337CBA5478EB984CDD22020DAED9CA8311C33FBCC84177F5CE870E709FC608 D28B3A7208EFF72988C136142CE79B4E9C7B3FE588E9824ABC6F04D141E589B3 914A73A42801305439862414F893D5B6C327A7EE2730DEDE6A1597B09C258F05 261969424F885C6B93B28E3223FDD3B040F5535D6AAE9201E5F49A143F3B65FA 75FDE4E5FB4FDEB79A695E89B66FB385A22222553A72131A7BEAC3F44DD0AC0B 0B566039AC5C1CB0A1304B882DD2497870AA5FB1FD17A704C4668F6F85F6E3CC 814D68758E24D9199B67A9395FD76257FE284913EF1B8897FFA602A54B39EB03 2A783B4A582A33F532481524A8BD8998A93DBFD4804FA77802FF52D5183117CF 80BC1398B9B1F9844EB62E162912873F37005CC29CEB7A2F0D0BD5BB237F61AF 6E8FF7D1D1A588E9E59D02BA0DF0B0C1D37A676C48D4C15ED295E86723DFCEC8 98D70775BD9B9737EE7C429429ED2C171A26DF23E85E933A184DC2D95C2A6F45 1530C5D40FD9270D4AD49D3CD8D8F0B1A5DBD6253D4C21E9A7716AB279ADA40C B4552E1F69F68AB1CD625BC2E48D3FC87A205B2C505CD956A7880153BEA8E21E 4474EDE7B9BF3796C1A0C71969DBF52EFB438C8EEA71CA325E65A08BEC02D7D3 ADC7ED8FC4DCFA7E6DC8F7EBE1425064FFF8135FD0643B368C0CC35059AC0FA0 10A2BD51896542BDF3B4AB53844EE1A75F087B171BC70836C30C609DCA54B5BB 066FB0814E6E06E867385DE7191C0FB14CEA8B0EB25FB03B6B69ADE955211C2F C444875097AB83F1C6768AF759F4B32B63F3EE35297BBFB79958DC43235E4FC9 26DFFE72F56DF4D4349BA7A7DE436F492BE91D7ABB098095925604491596DEC4 5E64D607C461631B4EBE5410DF56CBD3C9FAB92A722900A17D94A35F4EDF8673 2F41C4158A303E2B11DF3C6424C8C053334F566B39E22ACB22E9CAACF607DD10 5DCA164434C71C9B0B2947B0680C23B338300DBE87E52D95C0407BF3A3A9FA33 C434916F6A1EF0EF78EC24E3E14F5A0D9A4F9D61F24F4A18DB02033EA246870C 089BDE58BDFBF8C659E788D07C685303C6FE4C396FD8106989AC805B27867C12 A6E278EAEBEA6E408F425A89DFDBD47FD5C3061E88D6DB0E639D527035C049A8 F6E97384255029F547F5B492D05AA4F8FD33E71DAD567E46D8EAF4721EF457E4 D544B39CA26C234EBEF8D40FB63E6FD5DC5E6C98AEDB81442040A61094F565B7 5BAC2ED52CE186E770E7F29815B17D860E4E714C4F36D00CE7F30FBC23FBB61D 4CA7A16D43D96C42F7C9D5B4A7C67CA25D6F2C3ABA05B9B210B725A771B6B979 756311A9FB4E74B9B6067F6F7FEFE1B0E91F0E322C6D10DF70ACD0DD96891E5F 7F9E4480A96D03BD58E0A4B78E6AB4B1CBB453F3D721B097C39C70C5376DEE1A 7787F648C73BF1764A64796AF8542504F566CA4E0BF090C9A1DA761BCEAD4BB8 F789954182371B7041280F7BE0D1D0DA4F2C321B6129808553EC6EF8EAD9E5CC CE87FF07752BAEFE99CF8C29FDC1444986F9970C50CF1A0372EE5B8F4A5A4FE7 5C449A21A96CB0CF505BCA21F3AC65B543AB63546237B45DD7B14924263ED31C BFE8C751E4C29C569CE61E1DCFC443CFC21926316210F3EA1EB1DFCEC87B3D0E BF0835B59EE3BA9B9B3A58C59D9D6F1D11E97218F2EF7DE8CDEF17ECB51951B1 41E740C9CB337056C33BF1D937DA609E31C988AEB1A850564D1D50875D3D7CD9 160A17206166C17E4194C3FE3C9251C38292FE50B0D1188EEC0C4B6717CA3D74 D2A33149602F62565347BCF4AAFFAC6CE1F40856F17B23F9C9A5F6C44403391D F4E70E67FF1BBE8278E9BED6FAD464EFABB525EEBB78ACA702BA6AC8C7D2A0C1 E14C91D7E3C229F05F9C8662D09B8FF122F083F3BDF2E20CC6D1A1DB6B02E874 1E02AB36D90C2C164D6A7278B9EE0AA7DF3F65BDD148E0F9948E387D0E4A926F 14CCBC2325D02645FE80C1A70F90545FFA66D04B90C14E9010DB2CB96FC13AE1 8739CF477A3A0FFA679AE8C9C990B881703C29B8EECCC827323CE0E2E531510B A7A4026F10A9DBB8F89235B9617CB11E38952B7FC5C3596C1E49F19A7CB7AC22 DC16A83B67CD7B1EEDAF95A8165B0277DFF648BBFC1EAB5360319043746B1C10 D95359A697E17700069B4DFA77BDB4E53633224A01F13B63E3081D3F0FA96FAC E78FCA5F530277833B6DF5E7020023966880AE3F25176D1CB848474DFB5301F3 972DD96CBF08F012272EFAD55B77B2AEB523A82764D8AB789BB9650F2615F8AF FDF0A866A55A6AD4C17394433DB33F43477D34101A067C8630A5C09C4F02D989 A10B06C4BEB7D02D0B180447CE9911FF7778A9972F77542DB4A221EE01C54269 68185CDC33127FE9E10A85A3F3287ADA153E0835133FA759BF2BC53C2194B794 0575F8546EFF06233E5A6FDD2372B6DAB5C32BEEFE6FBACE911D630E5B2DA954 6A7F556879F3E695524557F185E409F0135DA474C36D492AEFC9D6240B74BA13 3211023FF327866BBB4C822C661D89C6C7C65C88B579C63920073CFAC94B6FB9 EA5EAC60C8CB087AD489640E28DC49CFD9395DC44026AD3D016E1CE8FDC39B1B 8A4BE7BA4B9EAE0130FF2FE3D0284AE8EB4ED6E2C5A1455A971279B76813B569 EB7DF7EAE576B905BC4A7EECC2BBCE421EF80CA1721D095DEF4D7B860D398B16 2995D2D5FD573324C84A99285A06F1552099DBDB27B1302C7E3FCA5AB41EF191 A84E0A84F019E36AE1DD3DBC5BE0306D7CFD66F7718B9A9FAA9436435D4C1FDF 03F58C8B3DA8C2E390517D53EA65A65D7BD96E971F80AC2C10F5E2A98EBF57E0 4E381DBC280A37D5AC654CE38F67E6065341B53B37D781E67AB563C3E137598E 2559D3587C1F6DD78AD169A7BF9519F2FAD0156ECBC459F38DBCA95AB3AE1B3F 046F9ED57AAE6D902DC6908461E091DA4A848CC7B1296A6DB0D97572D70B2CEB C4D69D1F35E62E61F27975251990AC12164A300BE7DA17999C17FC99CB78BEF4 083EF138E5FC50EC72EFDC9A3DEC37C3286FEFC9CF79FA794412412789D4F2BC 86C4F1E18A5B52F919F8F3A696515C638FBE294BDA1420985C9627C768329163 6083AFE9762ACD933104754DE0BD775CDABA75AFCF28455FEC469E068D399654 AB703D8DFAA6ACFD5ED21A66E0EAF024BC5DD854ECBFED7EDC3E660A4134E91D 931121A989EBC184DB3B59854EDD4BDD6B4CE97B0EAEF535AC5800C85FC930F1 79E14F6697B309477023B768D19DDD4EB8B011F810EE23BF6064E30F6BC8EAE6 1DE363ECBCA88EA762D02249B34116D00AE4E50E812240276B80893AD6AA89A2 1D2C07C8701FC01CAE0466FD76ECC59CF4B6DBA20FF97A95BA4BE307E8FDA734 D2964548BE34DCA8CFAC969D3E64AF57C264725AA8E62EB34B4C55FFD67E3110 C68CC631D51796E75D72FDDB9F79F68BC9074264B927F894C08C7AADD67B9FE8 A2D5E405949CE8E07086527A0BBAC59514CE8ED7AEE409EE2E6A9D9FB18D86BF B42CE9A2C385216FC698F2994DA26BCFE6A86AB6F27EDFC8D607DA22D6552EF5 3BE9BBE5EE64CAA151F4A0F8F8385172D2EBEF67E281338C5515A03DF5E9DD23 2BE10670A10400CC4E33250D69572C20F8C3160A42435B294752518B0CD7F757 3A2BB2CF49D3B8F2D98F127833B56286EDBAB5240D2327AC26E4D36B678AB8F9 A95D49659BFADCFE7DB0ADA770C1A5A2CA43FBDE923CFCAE0DA108EFDD1F854C 099FB8FFBE2991A4379768ABC8228F866D8D8C71BE084C8369893C78738B9CE6 7D5CE2F63475AA053A6D71A125EA6B8C1E7FB0189E1AC253F8CCAE4F91A42221 163E883A02DFFA07B129BF1A58B8683329F987903007D0A83D10EE859B8E6F55 3709A973DB4D8669C3C82966B41C4C376D0A965E152ACB9BF4CB1F598FE2288E 1578249188464C760D6EBF3C226220753ACD5904B35A7760C73A27CB80AA7373 2B4ADFF31BD70B87197BDF703E6EADA6B3F8CCB4B6ACCAB160C7252D73466ECB 6259C52B18F2693F0094C3F39DB4820D2D29BE20EFEB0D19326B6B91F3F6B211 BD21C2A5DC52A79B7F7DA330572E8E53A131F5A433590AB321BBC03A55EF0ADB CA37DCBAEBD65C6027885D6E3FACABFEC316A78D77133ABFAAEC102F33DF012A DF8FB3731747DAA84B6E0A70EEFCC5BECA981F4C3318421EBFD024B0FE6DED17 4F382192CB18C524014B5347C7D7C008CCE8EDD1DE2B3B3DA8F4595F1397EA45 EBB9A7B00E5ED79ACF88192056E93DC101A966E0114DC1F87822E9A4CEABB600 74823EF5E6A68CC8C85F44292987DC241EC34779CAE5DB6575E69794F10CD1A0 0C9F45050E229E4396B77B4541AC4361728C632C391E6F47FD9B6B081EBF0650 BA50E08F85FCE64200BB88246FBE975A95F10007C3045B263AFC326E2891E3E8 40C6A549209F31FBD7CDD1A70FC807CAFE52BA9D4109A231879637D1A2D0D811 FC8F8C6039B159BDCA88108CF44D789917A3F1FA8AB48310B76B6957748A68AB 4DCECEEB18ACEB7F553BD0E8EB576DCCF6DFBA9451CB22E056AD58E2264007F7 7DD85FE8C0760E76162486A18B4B51C94D4262E0B785B635DA8B6CE2C82E4457 2C6F01283FDA1111AB65AB3ACE72A14F7B32C2750BCDC74FACB7A27EE1BA6430 5B0963BDADE2ECED1047CA126F753826C5997B0AC0934ADC898CEDAE04D9FEA0 6C2C5248C4BAEED89280C57B3D622FC313C2D55C778DE4BFA17AD5C6259AB069 F7302F95C577937976C86E486E7602D0B8038EA2593FAB41B69C28A8EB6BB3C7 B474CCDF2BE50D34FD9B83B4E5923BD44ED8D0DE59DDDE6AA284A202F643EBFB 8D8A1F9116FB4FCA6D0F9FEDE700CEB608EC36DCB2F166F320924F1C45E66EE0 EC6C7EFD24452C9BB648C335A8F0CF6A5675F0DBEE2AFBCF3F433F8E7CC34E21 947DEC4095C97FAD6A8E215E88DD556927DAC886176D37A8FE27982F77C80D2C CBFD0A510D0E5731FDE7592BB82FBE7CA9402483E0C9E7CD7DE03EE6CF1F6880 33E78FE6EDE9B6C8743259671D9E81FADAD21B95F97CB4163AECFE73A59EC1CA C088B9B6E2EF04B8466E8FD3BC4FF194F76C7109EB06FBB05F827D67B6338091 F9F0FE1A00285FA1E19919B777E0D1911E62519184A15E2ADCE20B874F43F077 823D905CDB5B3CE9198437DC6E81049B143059B1A3A66979D3842B40B39DD4F0 E01CF114CF02920C519BDB28A9611B501FB515A2B0B8F32ACB80AA73626EEF51 E7DB5C613CA2173C7FD42704D7DBE8D1419CDA84D9496165AB46A3E70990F018 B27CB5316694FD9B6F94278CF894F7C31CDE03C7E40316269784181C6BBB7820 370A12FDAA3F26EF4B4DE569C40034D7600DDA5D3A97B90315190E2655229E09 A1C1069EFD864777C40B4C4B0582D33824DAA95FBD3E6029BA5A5FA27330BBC4 BCF4DCB8F3B177035DDC43AAEBE67E31A3F98A169CE3EB189A33F6A1BA4C7429 94054CE4A48617EF07B4BDE82D676A72E4050AA9F917BE8B6285B2365DBF0530 9DA12926038EF28E9BD48EC300766052D39B5533ACFBF7BAF1797B0484AF05CB 8DF9408AD6DF8D5DDF62616519F9795EA2649EC1CDF9C2B8E2FE5D07F8C3B857 8E86E483B784F56A58AA06336CDCEE65DD699EB30EE0FF286B89DFA70299C5DC 3A6F567A9671D60D347A372C4D884EA344519CD95DD9C18C6011FBFAD10B1565 1C39D67E53E3B7603387D6299C1B99E3DD7A93954F3FEA79B9A792606CEFD1EC 0F63F96B2F0CE5CC2C5B0761994A77ADECD2B18174C211B51D04E711E0C9165E 8C2FE0A8CA8CA784FB11497C9D6949DE91492951744FB12E2B2C8F3EC4A540D8 E5171539D03A0E008CB14BBD3E356C24792533EE695779B18AA29769A36F668C E27AB5A10825AC89E987FECCA3AFC65E125DB046DC0828066362FDC350D8BE9C 4578F52FBC76BB0D8685D7ED97DB93EC0684F0F674607DAFA40FBCB71D267662 E690CB87490FD59B5889D98B5507C010CAA3EB645CF58B072D6AC4BB91F56A83 1019C72B44C2468EDF551E5B6B10A727EC4F739495E3B4459F5097EC59A64123 C0D415203612F3F21A933CB8AB398518A2BD4EFEE0246F770E9F802BFDB8CCEE 1291ADB3E8F86CAD5F6AAF8B2304303977E643E533A071FC8D43F6420BB4EFF1 BEBC4D79997CFDEBC9B67E31EC2681E1EE9DAAAE8A71EB10EB2A777707884391 AF2A2D605E0DC23E9123CA313EDF39C51880A526C43E5D9D30565D1A45861599 DE29EB36FAE672324C663AC9357C2337C0B73F278BBB0CFA0327C1B60D257C41 5C96D838F6A555F77677378FD03DDD7ADA0A9D5CE8FE9FC35262F1E10D0C8B39 2D13987C88E6D3EFECE85B4A348E2BEC32CA39CECE063D8FB84746D973C78BF2 F23F3D1CB96FE465110BE031ECBE81BEC1BA5D592541C4560F9587AB1D7971BB 21E75AE8C23A110DD258105114E52A91812D279470A7236D392F463096940951 C6EF38404C68078708FA031FCC24070556C4ED093B1FAAF42B09A77E1814A799 1B3D8ED0AB7A7CA5FA30880E47974A84999FE7AF4B8DB66DA0A9F401DEAA2F02 9342B98432157A937AFFAA0951F113BEDC47BE7ACE1E37213A0EE2F83D80C778 8A36E8DB6DCABF7E6B58CE3FFB6A14D8C6A7D590744F403F203807BA8054F340 BCEEFFFB52BB39A68FA06FDAB5772D8613C5087BA949313BEE6269DF62613A3C D80EBA93CF14C8BA00495FC7854ACA5878A89221BC40FE3740ABA718F5175175 37C43E3F1A1E75B35303AAB9EE98CCBE0118411DB27EFD0600A47AD2ADA11105 765E25E6FFDBFFF29A7F4F8FAC6D17E422CB4E99AFCA2BEF7D4672ED274BAA80 4CF465A590511150E4D4996206F51A85E98690129D0F3E9A4969AA4E2C8BE21F FED0F8B4021AF636669356C1BDDDE4D3BE972A302D6B4657A859D72BC9AB19C7 40D61574CE8BE66B472DAD12DEE522CC421EE7E4472B77A204F4D2571E73F14F 755C7C87AB553A8E45467371C07A5D85C55031D3E7D1426A5C30231038F8604E 1B3D25DC0425D2BB956E0E6506EF55D8304750AEF6CAC154C7067F17CA70843B 4D6D7B14B776D3B1BB04D15DDD6B66D12658C85488FF63CBE6EF663106D75173 75D88358207505BC2D90B37DFCE16936858494EEAC8E0A899A9EF5353D81405B C8C101DFD4620F84877CA93EB7751CEB09EBD41278867A6024D5A6F91F96DAA4 47DFF0EEAC1C392CED53197CAE65E5A38DBC0D3A79EA8CB32A1B0BD6A59E2380 E9E06C3E71A0521A2CB6AF4A06646E22BA338BC2F3D7548930EBDFBDF58CF12B E5A131691BAC38EB7A69DC922E8DDE1E361E91668FC1FA38EF70EB073897BAF2 810976668FB84579A72C9F41F8885207F5150357CB99BD4BB1FF6D3F05CA4FE3 3A7E5DD4DB41F7E71491D3E5C84784644A05A68E6060E1DC1D027FAEEF32E282 83C06CE9EBA6D45F2F832A6FE180E3586D584BFB10C7DA839D463A01A05DB966 22EB303FEA4FBE51E476F7913C47FDD7624B72581D1F83ADA5E9B27863222FE4 5BF0E4D892D6FBEF9D0A27AF49007CC084B49065B586214B5F8E82A59477C388 07762762143002C4C3E4871F7C10F9854691460BE68948CBB9210B25DD6805E4 934C1B64BCD0846CE16B59C4CFC94C9BE5FF9355E32F6BBBA9B74800A0FDB7C9 9F489050703FB202C54456491677D001B2681AEBA1EBF2FAC2F84463ABFAC19C 6C8A1DB63C0711B89BCC9885D87F31A5F5EA4DC3E7B0B84407DD2243B49F0595 E96AB04E053381D38E858969AF9B01272709BB6E242837DDD3AC71AC0FDB663F 254C7558A3DCD8AD7C5B963E7C1258BEBFDA61F7CF174E061B58677502AE5AF9 47EEEA4B2A4C817936102706BCA423F0D9A9F49F4D072E1902643F9B66D1C5D0 A3EFFDA42B1EB1225E012B6EA9DCFC591C513FB4014A89436273E86063B1C056 4DE5344735467FEBEAD6AFD930D5DE1F7F88247A4E7A0DBED26FE232033F7D33 C73D381AFAB7D9E5F69704FD258E052306BE3B79875D124F8F875C92A38985DD 9394D87CF1E1DE67194E8D402DBF23D97D714E3BB63670780E766369494194D1 8921F7E569B2B7BE50FA5D590C72B2DCC646D852642951BD7C040A028A011BC5 326B2EDFE3B055DDD7556F3EFDB8CFF7C90A5B9802CD3725489C7FFF6097A115 7670698E37BC91772721EFBA5F0B2E86CF5D0CF3A67856E9B4456DFCB42B51DE 098EA1BDBD4FBE94A6CFAD34B12EE3F8D6C00807A5108938B2D3A84653050321 CF4CECE2B4575BB4CE339C32DE00E0B8BBB2A27D80AF9310547FE611B55CFC95 BA157E5075CCB1E8D15540665F48EB5E1B6478DF0213F7AECB07C23FB3BF84F8 B6B0213BD3EDA3716D8893297DF033F77E2796204C30B0E7C8AFD01E666FA409 92E7679AF11E538CFDF37454535D1E33A710D8FA5FC799BA5078D35549D9DFC8 E4AF5BAD3BD3D2CADDC3EAC1E4AD42F2F01F72161041C79F78D2A634860BAB89 BA8B399F559A8CAEE10F0ED48B2DB7851A8D2BD9FBA85C3A2679A766C1081E5F 995CAB330CE7DDF0A1E632CD3C7AAF6A67F85FF4DDE0C26B55D41EF138AC432B 3EC1C25A0022A5BAF676B5CAEE5C6A6336DFA921492DBA3092FA98B884600571 6EC419A25154E571B1A9CAA40D7E2A4DF0A8B8AB90B6364FACD68CD1579E7EFD A28EE5453103AE5BD7824924664255B48EA183B34D82A1F85B8648C3A6A59D36 C0DB3D94D687A789C4E26D2ADD0B73C67190CD5CFD0D789E4A8BE6D604C6477E 55B8CA3B278CECAA963645E042434C0A04B8EACD3E3F4BA4B1128E48E1B98381 A062B18FA26E09EAB09FC898CDB1BF12F686E551F4BD469984F9397ACCD36B6F FEF09B1DC04296E9CD7454B2705089C8DEE69B94EC7FA051B18606690A0B9FFB A5263E9F3E82E7DF6EF70514BD8407CBA94DE27CC947CF7C91CE867F99141115 63F5D8142E9B3754871289279682F244B1D1B3B1B369F78E5574EB6A7E6EA099 3680A74692607CB8343640ED47E10DFBE3338081892438061BDD7F8CCBC9FA97 AE0209BDD75134A41D82E4C5BCDD4EA08217FB8363362E6CBF0919B789C10A5A 271C4A4509AA2E83D42F30EA5B8C006774DF8CEB899CD573664DC733094D9FD2 12D0B44E726C5B21254A6B67E71FD74F00E9242F73CC76E29780F70ED0B6A1FF 0C8F3F676BA9C5F94E59297ACD707ECD7AFD041853132AD2E56AABC084CA6AED 7C6BD8A744BE89A2BBD9413FCBF4BC2A5161E6CC17BAB5F21B5CE00FA3C9AEA1 1A74A9BBEFD5A1435494F02D8C28F9AC4ADAE621744BB87FFD7C82D2E986917D 0C49DAF9384C7B716163720C0A1A4DD42E55F0027B11218E856555846D6535EB 4E2D89092A6BFEA4DB2622C28445B112F28329DE83068626CD0346D80F1BB697 A36BB9DEE91025BF357CE50988218AD211BF51AFA840262D96306DD96BFB78B5 B82475C2385FE5EED7531E00D6F8301570E06DA1BA95935E0B44059686A2697F 5A317FAD48FD9AD711775AF5B93BF78DECCB84AFA28D40C3F688D29C0F6849F9 F06C505F6E7B60231A60E6D5C69AF945199E9EB34F96D638BA6CA55F031A9DCF 3E1F3DD723217AC0D4D0753E01C05C09537494145C0C7C21B72AE0E998E28A7E 1B434E9454BD8B0221B5EAC2962085A6B7911BE0C0C9B65911462E97CC496A89 E9DCF30FE29E8EC6AB5A9158549F5BB9702D67E768195BA683A6BF329B36BCF2 4B8F1E1566AF739AEE0BAD72E1221F98514BC3A818D1571A06B70B99F57EDC22 6AEB3FC990C18BEC4308FE0FA68B4C1BFDA657969553C5723C12030329840DAA 32726290E1CF939AD1BEFD01703DCAE4B52C726E3EA1F30E48B3FDA4A29F921B F13C1C482781F2BD611FB6608775B48C4F1C56D606CE02BC803B8B7D6AEA691F 1EB76AF9B1FE942CAED10FE47829AB04A0CF33E5369EE0A54A470456FD7EA625 5B2F039A894E9D8B842EB579C7919040BE53DFF576359D17A952368552B69618 17DA9216591EC5444184DBC5F2B60655415D111EDD94D07859961CB3F5E64CA6 612E811A1F0553BD2BD05033276C59F4537B3141DCB7D4FFD05F64EBD9E995F7 0FA9E6FE94DEC98316DD1635D9A13C5BB7A4A3669F13648E145715FC97DC82B5 63C0CFF4972D18217C89C73CD7F296D20384A671ABD5E2DF1FFA454FA73A03C0 80880731A2E397890D3969B499C016F2174B6516F698C9A710AA92D74790F451 ED1E374DC709DB7567036E55E598B83CEDB250413D4B74E6BE9BFE1A9EFD0CBE 68BC731CBB58C25CF6D93192ED05A45EC2D057828B7331529E5D811278336ABF 57C2E7B5F85D30174F5A67977E2298293F57B406475B1E66ED31D4892FD332E9 39C7EE610FF0AF26396BED43736A6478ACB6D37F6EFC0DC0D86AC06D5A4B0C30 C390633D81C399887DD1EBEA28A3D4E3E1AFA85539471C8F4DD4FFFBB3459E64 AAF0692929E769E0E69B6CC20902F2082DC074B6E93572974FC088FE034DF6E4 855864A5E6DAE5D301813BFB47CC4B0F99C4A214A9BFBD71D14ABD988D9DDDB6 E85C8EF264BF7617CB4B98EBEBAC2B599EA04363C64502DEBB3F1C254AA02B48 3350AD75DAF89335AE20E78F237DE9C3F22625F6976790892237FBA88F75CAB8 63033CAA7267E538E7A65960F8AA477A357F520636EA1FBFE02F18F62DD94049 E22193FA952CFB8DA284CBDCC35848C0C4F4A598247338A85F70A896C9DAEF3A 52A76AD2585866A47CD995978FEAF6FD6F1AC09922A1CC837B2D21EC72004BD9 72B1892838C9AE4E08A55D06FC8BE8334D38CEF5F5261D3C60E356E9BD4C30A5 5B42317B4F5A240902F5698F8C2EB31B1DEDC5CEA589757F290FAE1718F52A10 945EC917E7372CDB1A4D4B30A3EB0287D1863E2774F9BA172CBD25C720A0A5FA D08442733FD111B6860210DEF22CAE8063F5E29EEF4D2B88AEBFF5D3723E8C78 F1F939C8DD5EB4E5BED23471CFAEEED4381728A81F4507236C0CF61FA59DFC8F C5CF648F963FED448CC1F534EAAE6E00522A0E2CEC8E85C5348A673D9BB5F2D0 5E8260C9E46C77ECC6D37644C5C4F9B7BEA2A69C2CAAF3A86D316A588B356CF1 5F6673CDD6D4FA4302167ECEAD45C1DBC7DD4F6D906A07B59ACEF602036B9045 7CB3E03579620F622D19D485C755D399F189787DB5D103506710FB5B5D5B2857 A69E9D827B122637732604DC813BA1AFFCEBC4E82F9276DCEB37779E25A792CC 7FFC5790D6CAAAB294757A9A14C8ED3CAC1EBC33171A90CE3C1EDF7C9C8FDB30 C0472AE1741160B02B19708544E441EAD8FCF56F03CC8AEA5591D2C1324A90CA A689C29CD456372BE9807F72DA2AB0768D699A061BE24FBDFB7C248848B12C52 9F61E4662126D1A0ADD2D801ACA92CF761EAFF836549E9E04B53584093C918FA B8C0FE1C8ACD3718EEAB4255DB62643630C93173650E80FF07A1A57B8CFF784A FF6F6B235F2B18F1913EFF3D021160868A27CB40AADEE024CDFD8A0E6E2FCA19 EB750D821D7439AE378818348AC9B8058BB7E2839C0B4DC0D444FF36D4795B16 FE93659D9E974E09C229D9B676C64926A2818BCFD26E2B241ED39670E87D5982 58AFFA13603E783DA3B8F302F2EFFFC770C444452AE9015DF3A5CFD4D2A20708 6B81DB4018965A0C7F70D818DB695AACBABC04B90A7AA25F2C5ABCBBFCC78DC7 E7ABF81282D2F16826E363A470F8071B4B800EC3036EB04DCFEC3E9935EE48A7 61A2BA0EBE32B3D289212C685B73E31C0D57282BE57C509ABD5670F0CABB426A 60201BF512599EB671885C18BD2F6A824AD7E40AD87B157C003FA2631CCEF785 25FEA37EF640A57C627AB51B8A1EEB97DD089043FB89241646F30AE434A7FF98 7F67EE8382B163590F3C9376B34082EF8DB7BF8E5545A2986575822286C2D414 CAA0DB2D2286E991DFC9BEDFF6ABBEC0E77ECA2844DCD3063B27D27ED490E536 3E69DF0725D256D76A989DA5F79DCF412700925DA49E02FC8A6B70B9D300DCCF F58292B0DC963F94FD8B0F9B2B568E3CC19981B9A18BEAF0193EAB188D70C44E 185D7608C8B54FE095D83A917784B1F0193D1C8237E949EAE1A606A381B58DE0 8DB871F24F7B8649625F3A289CDFA5B3537587A525E4177352A5FA6FC01092CC DDDB3E04DEF7AEF8C734ECB1A3C7A606AFB7BCDE02B4F2C86DFEDE75D6224440 94D6032D9F44F97925FCEA46FB13FE39ED4668C76D95BE18E6D9DF15C3527E5D 78632E1DFE104558EDBCD872C9D20AD3FE91634C1C7ED79F75BCAD8747E6B3DA 9CA9F544AAEDACF8FB811AB1BF10E43389C9AE7E957984ED0ACE7EE6E380B1D6 BB42A4F4E66145C9DB98C096586535441518AE3F46A7BDE3610FBA69F728B9AB B731D1D2BDABFE7F5FD01411E4F69A536C2FF22627D2684F844FFA6CDFCAE564 49913775241DA72F696FCE1ACA42C2B073D791DEA120A2B9A678CFECFB8A9CDA D6FCFDB7B7AC1114EB67AEFCA9B308E23A75CE0A9BBB72C4ED531CFDB3AF1E5B DE03F5B35F6105E5069D0AE4DD7C44BF66235FAD4F4870C32EAB4F8138502C39 D0530E17FAC5C94C518B064624DE1CD442405FBC1BDB74AC59E34204914061FB 70C2CE7AA2216CD1ED29166E7D6DE528DB9AEA2648EF205DDD8BC260538CF4E2 A4A398ED918CA5B7A8323904F34089973103C9A3D01DC0697F36B20D4971B495 A79B0C5E2FD4E9C06C5539B8A441AC94869352D5DC7630AC29B3E791A16D9161 1A0846FBEF9430DADE3CFEA0109CECAB0837632666451A74BEBFAC190E788511 2A36C8C311C9D285D58823327DC5A0BD4600418E199E145EA4FE565AA9FDD04E 0B3DCCF2594996AD780FFBE05E3B43A0B8480B31F1E53DC460804434902E4425 AFDEA6BA1EB0F6A17D1EAAF9C66C9C7CF30096C52F4BF270DFA81651E00D549C 256669DB2E6B63E2EDA3A7274DEB0AD462A14063743C6F2748DFF9CF56D27497 7F6C46C9AE751E91A6AD881EEE01E098D27316DBF6ABE0D4EE5A7B73CD288816 844861EEBE8941D2169C4BA06132FE3B0568E0618BF48D7B3F540DDD8226F365 A301AD15966AEA5C3F34AA246638C09FBEA79F08E187CEB4C85D74658D5AAA6C 506A5223F4F88E2B2D4F670148B5451E7A4C963357CFB5C1EF092CE560CCB10E 95D4FE03D920A035965E6B1F08D3C1E5819E9CF63F72BBAD7C89373E82045935 3EE58BECF418112888A04A5AF3A42A3E77CA5CEB1B602B8E085EC89D4358C22B C61D987572CAF309F6380738E9D1AB249F9C277AA0661F1B40A93D3E326F03D0 E0B8F294D8749E573F545D1BF97B9D66BEAB9A30CDE0CCB873C33AAABE5BD1F0 9BCCD54A58A9F8553475BDBAA30DD3959E27A412E7EE278F3AF74C645C9417ED 59C890AA8A060FEFDF5F5F5F53ED847859CF150B8DE3F44767207658A4FBAC5C 7B58A978D67D8F9906E8AEFF7830C582839E5CF5753A9F6482B379F676D7832E 4B12922F894A845EF998B470148A6450E9972527BDBC05BD13FEDD842A20548D B131121DFE1BEF427F1843964C9F19335137CE98B8CBEDA2003E86288EFB70F8 401820EBFFF578C2207BA625CACE786DEC3A262668EAEF79C3DE0B75F48A859E 55AF19C3DA13400D291B33C76DE776F22C82292AAFEDCD475DCBF2244A74C418 48F51AC9C69FA50C339C11AC0E5496FD1491F5FA4D6794C2CAF81F8B4842D549 530F37770C7BEBC37AA085AB75A03CF67C1D65273CFD5C63DAA8CB9268898A91 FEAE24418F6246F101ACC818E5FF24ACE6C1159378FD3E74BD02265224334360 60F3A435AE9A76DFF7555A73C22FF5710C9BB24CF10380A23BB1A14B46846A2F 1EE2416D7E2C472212BBB38EFAF28EC3CC19D431A503449C2F55A1BE515AB031 59AB01386C6D0E000ECD984DAAE84350B74E9F5BBB5619062BAB063C822F13EA 33BD1688DC1D071F64B9638038C0D6476A493862A111BD23AF54E1E673CB7E1F 4DA661BBAB79C1DBFA1217C8BFDDEA139BC72D9FCFFB6712D594ECDFEE693685 56D428CCCFCEED1A78D4A6C5613EB85665BEA97FBA58CE9938E2E889C2BC752D 8861B6CE7C4F4E4C7EE58C8DB9BE8F4419F4D31C9A023ED91A91648FFD8B852A A677D6E446CC27381039A79F5A3E8FEAD4EE6FC784423A6C49107AE6CB7FD2CF EC617739CAE238715151EA635A7888A97CE7B9ABA4DC579F527ABB4B59E63AC0 0F923FEEE910A2C40993E1E7FA244BDF25BF0031122895D1334F8A0E74ECB84F 7B9D7787BE137E93E5E608B47C9EFE86E56C982186FFD4FA5303EA377230D65D AF56E41E20AE777E2A13A57B78FA2D117D26880DA319222AA530F16FD7BF77C7 9D96CD42D1FE4F46B6E6FC30074D8E45E5655FCA1122DB7FD22CBDF77038A2FC 48733C28DD7F3226F95037607A6E156A5C87D8E3DBE9F8592F2691A9D06040DE C41DDDB05FBC074CC3D7CC1B1B18B1211E61B8089A75055253D13122CCA3979C 9F07681F4201E039E3D9F9AE2493CB382B787596EF8FFFD9A2A08939E956D328 F137799D1DF33CB2BBCA2DCE16FAC926CFB1800065D48F76B579AC1121B7DF35 D9FF3A2B6C524D822784FE070E69F752212223EE81DF46138949CF1D30F77525 EB61C40195F6907D51767774072150834E643AB539B6B009764FFCE9EDECB073 09086D6D52C4CCE54639DC155B4A6F14317198A75E6BAA070BDD1FC919AAA677 4F6A341579C1BAE2C447212339156FBA663833999B5FD0C1235AA629546C3F99 B77113C7D2CF535D834FDAB2E9A3FD878478D2213C91045DA32E96BB9EB4AA0B 3477B67C53E512E7976462169E2AC57DE9F37CC6A506FD1BF30EDA73DC0F300E 59763A48804BD808EA0A091FB88BB17E2A5AB1C19022D37F43F35CDB035A88C1 A0081C4E67267C649DE0A156D16FAA0948F9ED3C90572D033CDF88B03AD9023F 38982A47F80CAFA6E164BB5FE7D5BBCEC7AC95515BF064011CBE9163DB642F48 4319D8B6BD4D7412B3F773D09C5D2FEEFF147DED4D3633EF673BE6F0B892DB0F 44CB31F5B19501196FC0A3F64DACC5D2839B801F9C6A6DB19D644B66811BB522 D8BDA8BA91258EFA141573CCE90452C2E2663F000DF14BAE498A167556106ED8 A94420A2B12C42B488D177532F8C1128AE6850433B9479F428790BCA4E4A69A2 9EFF1778DEBB1A12797179086F9C876C98388466371CD9DC6F2DB52A1552096D C09F1AED04A88AB2AC3BF8602E77ED2D02E611BA600E12C19721351C1EBC051A 71030DC4148B21859B38617A9FF293938642CACB2A4243F8715CF3FBFD9E69B9 A45A0B111E172CF416DDFF831A0F938B809D78757ABEFF49428FDB013CA89E8D D0B69BD7081CEDB7BC3B49229A53F1DB7A2CEE54AA5E27CFCD5E20DE66A84844 1C5315A711AF6FBE2DF13376E25C869F371DD722310FC5084D9F19FC18FF0215 80A65EBF4B2F74235F65E51ED3705E8AC6ADDDE4902CBB18EEF0D2C0921CBCD7 66D0F79202EADA6086BB3C71366113FB8D548538E0D2E93D40BF63D3A63D1B2A E23D4317D5BBC09151A6002BAC87F1D9C67AD19C04ED9B6EF9A7F1C3A4CA1D27 CF6478E18E824A76F50D35A4D055E45EFFAF10366696A8AF266E9B77D7B97C73 E6407CFAA6D6C9B49DAB05FF1A983947CEB3DA891C3C32BC7D6E486EE6AA55D8 273D3BE9EFC7D46FD33B6741698913D5947BEEF94786BC1F1C8E99478E49A53D 7555BC02F1F70D1B63C511D76EEE1787A293F013ADA3353AF720BF7E2C2E5E75 2FAA721B2346AFC5B4B6B11D7652C9056F1FE449CBFF74A5434D8F46EEA8F06C DEDDCC41E9B27C85D41111DF5F3DDA53233A6101798EC8B264957AB5061F142D B26A12DCB10BAAAD63AECEDA565C4E308C83E94EAD96CF513B6E7C11A74FE282 004C48DDA746E574D38B674CA54C7266EAE2CB401F5DF9E6BB4619A1D20A26B3 59C626F32E090B5A6B30EF0901525C60D77CB7CE5BC0829EE4A76C0A28D2452B F7E9B05A2B0F793221E4D7939D7C6AA277ACADF5D6F833A60F8E92A5AEBC15F4 BCD36358C2DCA682F6C6B884A8F15135360A3D7FC4F614283F25926645DFF48C 2A1CB36D86390FACFAAAA957CB36E4F3422D447DB64C7E00B401A54C8869B15F 05A0CB3AAC8323609F44ECF204CE86C82AC74AB5C20699F4CFAA2411A9499269 F16E5BB19F680D5F9A3DAF6E0512444587D5C79E157D47E7A6DBC6EB5C712B75 B5EA260468A476996B76592A823EA065F9DA42CE708804E66D293981D7FFB290 6E52622FC0D1409C89FADC8CF3B18C2494666CA3D28FEA3D8BFE297FFA3A122D 2D1B3579493C7E9038 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI10 %!PS-AdobeFont-1.1: CMMI10 1.100 %%CreationDate: 1996 Jul 23 07:53:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /alpha put dup 12 /beta put dup 13 /gamma put dup 14 /delta put dup 15 /epsilon1 put dup 16 /zeta put dup 17 /eta put dup 20 /kappa put dup 21 /lambda put dup 22 /mu put dup 23 /nu put dup 26 /rho put dup 27 /sigma put dup 28 /tau put dup 29 /upsilon put dup 30 /phi put dup 58 /period put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 62 /greater put dup 64 /partialdiff put dup 65 /A put dup 66 /B put dup 67 /C put dup 69 /E put dup 70 /F put dup 72 /H put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 82 /R put dup 84 /T put dup 86 /V put dup 88 /X put dup 89 /Y put dup 90 /Z put dup 96 /lscript put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 110 /n put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{-32 -250 1048 750}readonly def /UniqueID 5087385 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D5993DFC0930297866E1CD0A319B6B1FD958 9E394A533A081C36D456A09920001A3D2199583EB9B84B4DEE08E3D12939E321 990CD249827D9648574955F61BAAA11263A91B6C3D47A5190165B0C25ABF6D3E 6EC187E4B05182126BB0D0323D943170B795255260F9FD25F2248D04F45DFBFB DEF7FF8B19BFEF637B210018AE02572B389B3F76282BEB29CC301905D388C721 59616893E774413F48DE0B408BC66DCE3FE17CB9F84D205839D58014D6A88823 D9320AE93AF96D97A02C4D5A2BB2B8C7925C4578003959C46E3CE1A2F0EAC4BF 8B9B325E46435BDE60BC54D72BC8ACB5C0A34413AC87045DC7B84646A324B808 6FD8E34217213E131C3B1510415CE45420688ED9C1D27890EC68BD7C1235FAF9 1DAB3A369DD2FC3BE5CF9655C7B7EDA7361D7E05E5831B6B8E2EEC542A7B38EE 03BE4BAC6079D038ACB3C7C916279764547C2D51976BABA94BA9866D79F13909 95AA39B0F03103A07CBDF441B8C5669F729020AF284B7FF52A29C6255FCAACF1 74109050FBA2602E72593FBCBFC26E726EE4AEF97B7632BC4F5F353B5C67FED2 3EA752A4A57B8F7FEFF1D7341D895F0A3A0BE1D8E3391970457A967EFF84F6D8 47750B1145B8CC5BD96EE7AA99DDC9E06939E383BDA41175233D58AD263EBF19 AFC27E4A7E07D09FB08355F6EA74E530B0743143F2A871732D62D80F35B19FD2 C7FDF08105847F13D50934419AC647CBA71DF74F4531DC02BBDA22AEEA3FBBBB 407E0ACC52BDC60D01A29407CC4F93EB8BF6D4813E9BA858D54F38918AC82720 4956D50291F0546E50FCAFA6DBD0099123F5ECD4AB338DB310DB4CAE11337A89 8ED99B6F483940C97544F888EAF0CBEB11094A13C073D0061808662A04A82BA0 AD35E8782F854AF66C20C0FEF18D0ECDD1646321B93D327E53D88CA0E825FA95 05AA57BD7424F8547FBCF1286AFD8C09FBD9A018153211C05BC21367B522FB53 1770EAC3F969E2E6910A9C5E383120DAC6CBD8E3B7E64E461BF5267CF23DC1B8 C85175C38C3D5BC28498F99599709E13D6CEB29EEAE662FCB3E86EEE1B6BE118 2DE35B7B08E3C836D9DFBC125FC1D201F0D44A13A0C387167A4EC1582634EABD C8E9323FC2ABAD9A64D11123821AE66B695F5BE50630289F6F1D708FF7497F84 CE25B74A99A0DBE1CC08D0774EBC46FB05D7AF1A47573E0CDF692452FD68BF07 62941B92188CCFB75A5349124ED55667CA6C5D951CA5CEC834B00BF238C5F165 A30DF8C65F21D367EFFDCEF341423397F259F007DC828F3F0C383894B6847F42 3ECB169A95F5A263A5B51C16A750FB377756499E5EF92B51DAF9D9567DE22703 BFFBD655046B27D2408EAD1203C1CFE0DB2DB9FFA7FAEA8746635FC5843F2944 74D744FD7FDF925425E5B41E6FC475C749B291F6638480CB7148FCA0EA9EACDC 1FC1A221A87810119E02AE91122216B1AAC5A1FC105ED65241A09C8FB39A5DBB F3B742C4C67C0D09229122F3744EFEECA1B4C2AA1B258ACEF45F788CF0B946FF 78580A2ABCEC87D7A84F107C8A87133BAC8D370A4832FD71E0A7FE8563CCC6BF 15E825735CA47EB73F2CE481E630D73CE5D06B4CAD07D5030E4D162FAF7A69C5 859CED6C9CA78957305853EA5FDB129197E4DC200F44C9E17EEB2F88BC5A9B86 BB729F9FC5508D099E673200BD9DA0D187E4369748CDA4F829079B57377F4C26 A5ACEF3B4EA625A48844B1F76748501F63D6B7FCD1B6B5D39098499284F991C0 A72CCE5281ED38F9EA62CB359AFA9D90911F1E2B4C73F94D8578A1BAA2BC977A CFFB69B5384FEF224D0B599B69FD67916250ABF04601849DD46EF17717E25A19 F5DA2892CC10BEB453FA5FEA57DB8DDD05C18EA3E5732E91D7D1C0DC20679CAF 5F8249039E06F322669C5753132864CCD084B8A43F3E520C509C1720464B63BA 44606FDB6D1D5E3D0744E12A5678ED9FEDA42ECB4A7164F9FA46829A094316E9 B6987814338F6CFA8FE016CFA77CC3E9392A4178BDD0BBC9A616AF0CF8B5367E 80DA9EE535E3A092F90FA9D18D11656C16567B920C8B8C0B37BA749F5518A784 11D80680D682639C44AF74BA6BD4F023C0B619820BD21E647B34562E7B0F29E7 2557A48DD4C70AAF9B04AA2847824550377C45A3067F1949E4C43FE24CBA73E5 B3FE3941BEF2EBE30EAE2D49914AFB93B2A7A63838CFEE098C5DB9886CF31659 76B070BDBE46BA1BBE807452787B2A5EC82C6C9EF0567FFC599484BAA07AE396 2F51EF72C270F9A861615D21A5C3645A16B8143E8DCAFFBFD6EBB5E12E7341F7 7D3BB1D8383FC5855C94FCB5898572714164EF87460C39B400E9BCEAB08502A3 8104FA93FF18A7E85FCA60AB9193239AC544F7339985A282180BD9A825EEB661 3F05AC33BC58927338C99501E24EE2C05946ACDAB8AAD322177FA25A7D967DCC 3AB5C3B19D9123FD91585F408F9E57D5402257DB2392D928983D65E1FC28F65D BCBED6B025A8E046654B9CAC92EDA1F5F5B8EAE107582BAA4396F8FF5E4D08CB 611CB3AFF962366BA5444B20E5F17FC582CC98C4416D3CD19E25B1E84E7F396C EB3A0DA5AE5DDC534BEC0EBE8337501D057D64084A0152E3B7FD952BC6D36ABA B4E1A0198D74DA9136630E6DAF5BCBF9D5389C2C77307F7C35BE3CA12B63317B CC7B1AA19E70A1B8779FDD39D3082C258F911D9EAA2F36D58143207ED1BEB1E8 2A896F3741DE569D35CAA6810057525E499EEAF3DBA2CE74992A4EC529DC39C9 A73234171931EB6038FA31E27156F2405782735A003FB4C00CAF690F564253F7 67A5E9757B650276EF993D0C79B23DFC2FADFEE16B0C3621678B08F011F53D19 2C450C40D4725C433B6D0CDE7390351E0AC45A02173F1640F470B8720E9E6B7E A8AEEE8F554A1FD96BB435C649EFCE7DB65A302D62FE55214551BEA59944E7E5 B383B9BFE8FCA8B7DE9339F3C6A92CD01BD506CACF7A02859FBB4B7AD298894A F9A9583ECCBE65E24F9F1A524D2D929B1B40E6E97654F2BC7C5F334DC095EEEC 4206B42DDC4E499F8B5BC6838BDFD58D8054AD09FDCB05CC90DD333C3D393B30 9D8AE88E88E9EF6EDE2EA9B8F4BE43419E174BEE872CFB62BA0A07AAC660E1EB 1527E3C0F26CA0A2EE0A124C2E1752AEC8186C7D962111484003048C4347B071 2EDD8136716DE8E4343EDA3EE3092A2C771646E9DE595E021E4B28F18BC74335 F82EB6F07B78947D29451C2A29E52D9FABB621907CFA0F9C63E39F4921450AC2 AA497FDA09F28DD9ADEE4721A2AC652D5722B6043175E94A3F9749D2584F1A30 A425F9626A99571D812F333C45B206886EA08EDCDF4C21DAB530A17BD7DA4194 6E5053F6342B27E17DDCAE7BEB354B542C1A288DC412BCEAEF58DAFD67DB6C37 E4473163B0C43EE35E6E98F367B8B9D570589B2C4F44A66E544BF67DA4892D8F BCE8FF4DA18D60521DC50D032848E5D14BE9937BF39F35B1C3FFA92636D8CAA4 38529F92B3EAF48116421466E93FD52AE915DCF3A5F037E8C26C21DD90F1DEBB E1B5B71D35714534463F4B5E8230771EADD2B5264B327EAB11AA04F2A2169F29 13E8EFAEA66B0AE4838DBC0B360F4C7FF7B231C79CBB045C34887B5ABCBA965D E8CDBFDEF6B07EFCC0E0F6BA0FAA18D6A69E959B5508A576A0C56CB2C574DB8E E7DBDAFE9B7C221A4CCD2EF3E429DC61A94A8738E97CF0442DA31A37D7963207 63566AB19347F968A4A526C2511DB9923015EC7EB4DCF602D668D9B263360323 73831F9E4D449FE97DAFB260D201F6C1D834DB0F828D447CBC638095642686DC 451F68000C6CD9FC09ECA3E4F26E58BB025BFEB0FA56492812D293E9759CF40D AA0B1D3F54FA6E31EC6C9B2E030F6670B699A7CFCE8D058D7D6E0803F58BB4B3 FC047076E384242F44D791E33B655603FCA36351D623CAA98DA23F6A51634827 7A3B68501CEF58818601C163E16AD7D91129A62B4DE4FF552CC9E7598B86CFED 7B0294B2D0A597BB927E1F081D0159D683DDF65DD1A001D07E03B23CEE990C27 F612442A021C84533D145135E70F5E19BB219BF061C7C09086AB4D6A66796DAB 6D3D359730E854EA56BF2724475DC7202FF71A325E57EE18F3B3AF4BA3546AFC 949F432401B419FCFBD0399FA01FC8C02769E2D2ECA9B4E560D445FA5057B9D1 613ED52859020FF4646ED2CBAD6054C1B59047EAC6C65153F7D0BB42EB9F164A 6B8CC94A8288975017FDF6DF33C7B17323D1D01F19269873F5A7D50C183889BD 58807F1742289E3DCF332E17FE9A71C31B7A2FFFB8F59661097FD9ECF494D444 5469EBB2ADD5582EDC398AD421919235E6FE44F0745343CCD2755944CA4753BA 66C8A37A1C023FC5B3D697C01236E3CD38FE431619D3BFAEB9FB2686D2E64040 1809399987B9776473587C0F7FE1D8C0AFF93962D38BE9726D57222218077144 196AB402F2DB7EEF91EA2697A9291717F17E2FB1FF37E09D6BA5C13DC2DA027D B68739517A00DE5717F440B69AD223057535BEDF89E88B07C77BA9713B8607AB 66D305FC1CEA98FECCAB7AB526D0AFBDDA371EAC6A0A4EF4B17E1AD5E6BFF4B5 00872D595CE5734D606AAB5E93AE9E899137B61D98C5098AA2ABDEC67BB3AC87 0FDB3302FD60E9A641FEFAEFD020F048179616118898760A1FDFC4233BEBD103 E05D5B862344D7D8562A57DF8EED7C16F72F2E0FD611B963160C020D3BF4F5B5 92174615649595FF913360DD3B990D09218BBDC62757EAEB548F8ABC98695833 1B14B3FB02763A2DC03DC41FBFEF46D27E89368A7C8192A03049E87C3F904FEE CC529E2D4BCCB05315D6C1B39551C9FCC24FAA8962EA6700954CE1A53573FA44 E0FA64EB5CC874CC881285BF591F7EDE4559B620DEB353345FCF39A2DDB90241 2B6E8E0E742D564EADABD859D976A51ACDFC8506DAAF2AFCB5623DD37218D563 FFB7ED772A923F54C964F1AA7B645C8D53C7C91F498D9E1099057942FEB00337 7B6DAC9260562FD6869ED2C17A05F6ADB8D0BAF11D556193DC062FF8E3B1F909 91EB4DC63434EA2825CF0B7D0C862556D9E2526152903168928139795F417755 6BD1835CEC5E25660A230D1E37C54B60CC79C1D90C49529035DC715BC87D1E47 03B1993AD9DFFA7F944CE46C03A713C322EA07A60BCA5392BAA2D4971A139015 D7BF7C3DB2CD8033FFE6DC29CFC310D374B93466F4923E655C9BDBF60DAD5DE6 47DF18A22F253FE4973A87F6EFE292A6E4B179715917ED0E7C08384BD1512BF7 4725F796CAD57A939C194E173BC6915064AD75C261A75B442ACDAD39BCBFD568 B7C6F198CEB4F3B657F49B0907075F96C1A21E744A965D5717BCB3B9CB12DF23 ED3166428DAA5A867ACEF20E65E9FA61DD3642AF90E8A314A49F4A9D0BBC6088 AF8093BF9A346AD4964F2CE89B2A6D040FFDB91384F72329FEEF1FEC2937DD50 601D9F33BF7C45A73432B0A2FBAFE248280419AE3741F0493D062223BF6C143B B2EC432529D0AA269F0614A539B658ABB7FE4A39ECCFBAD44D5CFF66A45EBB0B 8FDA9902BE6AFC2BE45B499C19734434F729F7C713BCFDF49C45F2440EABD4EA 079C6D7C85AB5EAAC57CD4D43FEB2FE60117FDFA8D532FEFFF69A6E86B179888 C443C297C09D7CD292AFB27030AF1D99BAFBA9CCC478F1A12B555DF71A5852FD B365B35EA399B3AF897EB79823690CA6E48FF5E22B7C13B8889F7B624446D447 0498C131BFD660571FB83B6016DCEB869A4810C62977D748C1C9AE6AB790D573 1C633FCF42393E6F06BC1632E0AB906054B9D59E31602E66DA41886D238F5134 9BBA3DF43E0DFF920FA79A0762B6A573D3AE037AFCEFD933F8DAA1F6CBB44D52 ED53CBB9A4C4F2DA497276E772EEA4F46D156EA48EFFDAAAEC2E16DF5235FAF2 F78B823BE8A42EDB4B316BDEDC570EC957263F8108F955E2E37AE33186ECE9CD 1D765403CF03ADC2F8388C9FBDDB63143B9E1B16D1301D1650A13BF5D465A913 2AD1D045E594FA7533688CFE6D6E2861060B9386A3E10AD815EBA9E458E5E2AC A7526DFA7B9C9191EC608B53E4283426BB2D277E0E8FD0ED33DB7FEB767451C8 6A94590BAF8F1C2F81ACD73B777187275C659973DB8F8075C5C074287FD9AC86 2277CD1BF21393B612F456331C422BBCC1126E04A19B7FEF8EF67CCA7B399CA3 A515C51BFEE45B595009C748D2618F7D316338A21087C31EDAD704DB125D2596 7C48EC2BD6A76BE1A11F50346FDC1BE69A1761BD08CE41F11F301948E446C843 C60103FF1FCAE292F10305D87007CB8A8330B6A35519686016FE9121E0D2379A E1B4109D345C60C117D80BAF759F3BCAC29C6AB9486F2BB70DB35B66A15E9655 C6E5A46EDDD3E6170CAA92D85B336F47587ED19062A47C40F0C5AA9BA0E06656 D8B386326EDF8F698BB9D31CC1B07D74CDF5A1E404E10088A21530C19DEAC1B1 FD0BE0DB0B7838E415A9B47E08CD5B4438C3501C39CC2E8F437BBC98B5D56AC7 BC6608FCCC2248B3F17C647073E5AFCC5EC52D4EC9AA34A18CB33E4F97DD80A0 0A9E0829E0ECE4A18B9EA87ABB7F5A48CDBB68000FB195A186EB63DC81965204 28C95FAADBCBAF2C625520B45F28383094E531733D4E54A61C2480C62125BCB8 381C96071375E75B1766A5130044AE0557C13E07402FFA35F0A01A515FE4D178 A202A5757D19A4B5F1F495B5DE863F30034866F31C7645C2DF9DF2C59B6005D4 3BC83BB0E2288A23C2573F9CAE925519F4C8BE8B1EB88625E46205234C99523C E0E1F12A173CC8454DBE1A04246E3B6B1D67A64D1333CF2E2B6605C50CB03014 F4756661330591E9CC5B965AEBC887C83B7D9AEBED96EA361C5A67714CDB352F 796DD74145C2BFF05A29E65CDD9D3C09DC8EBEF22CA3B12B343F31BF8494C17C F3721087E82C497867B9123BE20AF0B56C40EF637FA3B96683E0FBAC21F09FE2 F4360905866AF76FF05C27E77E9FBE0B4405A17AF9E40A1F13652801F0E96687 D8DE3FF43F255E4EAFE2D13F5342F4A0CC66D990AFCB50FA34763C414DB641B6 943E8AC54DC31570E41CA4A8F4A9BCF1E8432BC7C1E813EA2F24CC9BF9AFEF95 CEB183CDC1B409B091C518D2D007442D7579012AB106F18AA928EC936411CE18 CEAE8BDC544FA489C3EABB4973FEB2D8307353FE420DD9832408E26C8690B4EE 364A927B19BF6EB1D93D536AAD0EC8FC7CB98FDB0054ED0A0A9D2A2A7ABA6CF3 06209B6C467D11B7EBD634165425E3751C25229E9305F4E14B7595B1B256D714 E2F7050EE6BF560A93C3A52ABF776E8BE6AAE67D1C7E6165E571BAC96CB34F0B 9EC539A08EAA3F81C0BFCA576A8498B01B9B4C1D9375A955177F98DFBCD0CF57 7191946E49593560F7EF04807AB9C211D80D98EFB2EA4BBFBBCECC8E265F4986 9093A3ACE3CF91829D29D2418F6A97F04DC91288594C8DEB187561FF96DFFDB5 5AA89EC64B8285560DB350AF9B2F0723C73064B4B57ACB84E678A23E86CFF5CD FC4F3FD841425A0A2BCD477B721777EE343B3AF1BEB47C4F40FF863914568F12 22EC543446D4893CFD9C3D8F7C03B9270DDC81A5756BA0DB5C958A158C7EEF9F 6BA0A5C0A0FF3DA879FBE81661A9C32905034377CA9A95A3267561587574A4E2 32E7F7817C803E197A762643DDA5B3003EC3DAEE98FD4F86E793EEE4C87038B3 366CA76476A5A0DA40C1227986481BCDD39FE95B2A4546A8BBB1AA7F9C74B151 AC9F31E9D3FCBFCCB74EEE1B3DEEA5494788147490ABD9DF28277A51FB4F0E94 0B99166C9E8D613BED5B59AA486A85BE5CE6D76DC83D0CA97E6AC3B4825CDC8A 6D5B0394301A43B2A3385205122EE2F9233C9A2DE1A65DC02E8E6CBE95B2DD7B 4EDF195C8DBDC0315F1269CDB8D594436AB09B042DE729FBD25C3ABA6D9E4A14 81CCCA2F0656B04668BDFE88B60AAB5728CA000AC987FC0F9B9E3A7B9B09BE84 70C2D3348CE0D0698A80FC7CE6F5D3C396454FD346D6047826DB31CE6AA82415 5197201C7C5C76C67B9237D9667D1C5B6DE80BA2A28F3805386C1764EE763D65 2CC892F4AEB913AA13A2972F9BF67B0C3C8E944EC2F490B65ED91F072CB70C34 C2A3059F98D6C8F8D86EB041E6A845DE073DFB881DE03D5C89F8886CE9C82214 D279C6F1A3FA77D7B9FC1F5BC7ADA27DCA9B570F8086AB7F867F54CB2ABE145E 7A4F045A63B32FCFD3F7F6FD38DF83F717B30D2C88D346B37881B9EB9B72F1E2 1EBD0A9D1D287B7F9B6A22A15E527E64CD75CD64194BD30CEB9D6A657B1083E4 6BCBA0CF8CB46853D12ECA9B40E01C13DC36CE6B99100959EB33654D93686B8E 0D59A227D6227853FAD2F39D052BF3849EEE7C5356CCEA931A64B990FF8DB88D F1F6FE0FB9F0A9ACD0077B75EC7D22338E87EEA4789DE8EC2CB0785B372A02B5 AFD68FD6E8A1108C568722C2549D20BCD41F00E2A0E06A32D58579C54085F54A 6FECDA15830F5783102041A516C57F9FFE43E5DC85AA0FD8468955EB08F5D177 B1F27201E520B5F1370ACC13A6577EA971D5D51C1ED2498029EEA01E722047B9 9CE46D9C598B71A46F86BBAF8E1587ED726E6D3BC55ADC9A8A20D98C5C7B0A5E 570CE28DCE4DA5E8CA4E77BC60C966658C2BB0E1D7914C265DE0B22E0352D517 CCCA2281A33A5AAB5916A0A58E8CFF08C4BD23CA8632EA496409785A6891F3BB C092B57BD47A9C228D61820C6804AEC2EB75E965BE5EA9D18097805D95DA55A2 879F44346F8E66A864CAE5D4BD529B6291262BC515DA722C253398A4B622BFE4 C51E6FA1F3D787A6524E33194EC4418F630B5DF350B3C922D4F9479EBE6CAA0C F5182E451D869F750A56BD989CD0224E7EB63AC0953F3DCF96DFC4740E9BEC29 2C652C8A29DD06D2B82146B260374DD2539AEC990E65325EA9DCB050B209673B 5259CAF57CC95A5D9449CBE8FF3F59D97C568FBB4100ED162C239D78BE4FAE17 32680B3ABB357A07AA0B9310C6432A85D69D0AFDD1405AD7195FD2A2339235BE 1B072133D7D48C453A44ED4F6619D7FCA060104B8BF67ACF5430700981047EC9 7267CD2014199E646E62ACCF728EFA23180FA2A0CD273B52F89B29AB3EE7726E BF67766C2EDA035D36079DB1B80B3CC2775B0F8547992A8E108E2D5712BFF254 9E243821EFEFE77F20576CA07E26E94E2133B73261E894065688D8BEC99B036F 12AC84C2183BB27D7D0BF67D8BC3821BA9D9625D05700B318280280A4F7B5B9B 1DA6EF2D7EDC08AFBB5EE1A813F965F18063858DE1D88417E516D2EA21C0D1C6 CE1936367E963CF5C78F76D4EEE765EB30AFCBF69167B4686051254C629BE035 6B050B34E2AFF1961AA5924F4702A29903FD5A2C138D6DB925549FFBAB7263CF FF54FFC9DBD63398619A7B3C29B7BDF126C5E2448C35DE4FA428EFEC22A26642 58698F71A278EB9931B7C461DE623DA1942ED36CDBA7B7DB0B8567437A08D9F9 F24E29AF23EED18AC39E939D09D7B226FFB53604BBCCE37954C44A40E937A552 41489AE1CAA3F22CE3DA9C0E37B35D06C6A0B04A36B3AFCD15CE4FCAC15554AE 400B64C6C2FBC6883E0ECCB35DBE34E834198F9CABE9643B5BE615083EC520A1 A64FE80493E20B3AF17ACAB987172BC99B6D7D75E16BFC5546F29E89801AA8B8 5A3786B6F60163B4E6BDB5218FBA4BCC6FF03050281357601FFCE31C08F589D7 9A1D6EC06F2F6C7E2C8B4993F5DE5C4D0D1C6BC1366AFA50EDCEA7378FF1FE5D 1E929B22001A5B5E95CAF3D8DC0D76829CC0652255F15BCDE8A681385067739C 3D6AFBD0D9D9B4DC38D28BDF5EF466CB6A558A4A195CEE31C6BD30824E7F7152 15984334CA3D19AA0CC301C97877D9B715DB4E1DF4089CD441FB2EC195488ADE 5EDC46221C4E66ABE88C896D0DF7D934E6B84EAC03C57214FFB55F677208775D 00141AF6484CD0FF356813D44A86AEA70922244C833991DB9AC233BFBB40B93E 52A70A42E8A70648FF2DF4D2608A986EFD146B916B5E481A4875DEEEF41E2824 03A65A5EB29E9383D362DFC5438E087F3C7F42A0A590144BA3BDB06DD5AFD109 97C5021C0091D1BD45B5A570C43AFC37D07B55472BACDBAC74224F0FB28A535F 3CCC0F8BDCFA12090999C2F2857A7003CA1D7C9380677993538A2DCE01177AA9 13AE5DB495C41EBE204201624B48B997B9817106AB3B77D28B804AE87DE23DA4 8E70CB2597EB3E1345B4B1196C7FAE5C3DC0BE817FEB1B6263BF98B7908EA9C4 8B1DB1FB7B8539CD96AE90FFB406839A00BEC071F4DDE2EB963DA5EF7278818E 921ADF3B0568A43E0DE3DDF0DB245B070614516EA22A96F0CD1AB4BD6AD51D66 35DBECD4BCE9774C855631FC14E30464E1F740DF192B62B1B111B95ABCD2480F 0999AA27E523B4D8FD092C516C82F35C30A92196BDD6C68421AE50B0CFCBB480 62169CF673319C406EA29E9178CE43D55388D2A87621856AFDC53C0E28410ADF 3CA534AC4271AB7B06C43446E7A14698AD626D75009C51918CA0705A30216BDF 66A8158D6D80A39CDC60FA69B12FDC7B271E63FD4C24F32FCACC5812EA8BB2B9 6551E7877404885EC3A8BC88FDCB88F0CC8AB912623733033F38726F8BFC9AF7 68EACC949BE0980A6C5018F43BB75022280E2BBA1263AAC3B0E658D921192A0B 01CBA17B2E2CA20863BA47950296C57ABBB25ABE97AEC52D74DC99A219C32223 28DC18E5E1CC8E06D75D681093A7354C9F6CFFCCE3765FE1B2FBE1406AB81B8D 441E06E72B25E672C75EECE8E05CC451AC4894BE6125C6CDB56DE8834F890B5C 82B7627251800C0C83641A1E010C98E0F815764A408629FE53F9F04CF8D68589 F6CD52361B0652278DE2163732E66BE897A34714BC4D73100D6CD6BA99291A26 23E8D29E7E9A86C3F9C2709FBB07BD1C2EDAEFF01033679C1B991FE2B8BC7753 77ABB2D4D1A2D69A4E4A3C204F0A483E9522DD687699B4644280095043B9EE43 209F0D383F1620A9F731405BDAA067E8557D39A6B154F1C2B2EFAD23D9A4C55A 4066761EF3EB5639B29FC5FAC22C70F42E4FB6DDC09D0607C4C357A89A71E8A4 F4B5F57FF4A238541C6D515E5ACD10AD15CB5F0F18448B8829797DFE48169A87 8067D85CEB57A1D7E5004460F08E16A0F1A4687676AE92BD9AD03EA350E1935A 7F572A086E713A230160EECF8AB309E88472CA0BC08B95BDCF5EAA8F9BDA473D B340CD306E00F50104FA0AF521C8412ADF484DB0577F90E69DF662FFDDFA1C7A 9B6FDD030BEEB04EE1BFCDE004E8E197F38D64ABD40C781D0CBA5699A1A1070C 565FA61B618668BF44411F37AAF01B59ABF5F67C9EC6F6E3F125D0B8EB6827BC 925E9DFFE0EEE744C52FBD1372346CFA9CAAD6A744BA082F2E089A11D4B4CA79 020D1E3E08341CACE9C662734240E4B0742E301380EB8CF0A3F0EA4CFDE369C5 189DDBC3267A82F32CD0D0FC4C4F71C3B1389F1FC8457C78AEF93326042AD821 09DB4A4013F6904E4845C74790DCC26667E680C3E9094D149F901E5BB0556DAC BCC84EB43C3A46D655C0206E5A8F538299EBC1537CD704A823A20BB3D8EEFA91 C7AA2018B922AABEC9F8B1D320E98ED7112477B7657A857C519235EF59B8E418 22FBDEBF06E7BF60E4BE880A267CAD40841469B3E26B2D9994A16C5AA494221E 3D67FDC2EE2A9474C19FDCCC13183D36E3E9736D82D4DFFFAD51D0BB7A3137ED 85D5CA0A2A195C322C6A4ECD1F4CAA56D89E0B29BDB8E86E98A3BB10C5682091 3DDCF81E1B67FADCFE43E253A8D3DB65A99750D10A86D4E178566A2066766651 C7BA828AF81C391D638C6D0A37CCC879320D50DA12BFB437172D0C29183A0132 656A289A2EBDDFC44AFE74B14E55FEE1588CC41630CFD739A262EAFCBC333D92 DAE8D1FAA6B0FE72107E1C206F207244BDF1BF73C5F0DD6F58144D2F197E1B3E 1243DE36B795C5A004F7602B86070143BED6F84A6957E33DAE9CD83ED0630964 A2ED49E8702068ADBBBDAC750F5ABEF35372DE3B4BDB37E0B2E6109E991B80D1 B4C6E18B3179FF7EBE69C6E711EFF9C7CAD29C0533F404168B5453AAD169359B 409D6E7788F63AFDEFBE1EE23B402A02DCF472FCF49B13E26816620F2D31B2C8 5AE7CDE15A5D1851B0D206BEFAFEF617B5E35BE00A1BE0C2C06B6076D28A08A5 EC2E5D51812BC5F924BCF53125BFD0875C85CD3550092686F755C94F95B5D886 C302272BAC3536B940FDC95BE28B77DFC89B7625EAA252C4DB7C3314583AD0F2 220ABA215F34059B534E647331B7EF48628B8EE4AC37852FD1F546A63F394C51 03BA2FF6B058FE263A71CB24D0B0228800D101F19D9E1147C81FC50512711D3E 9F173BE398509244E6A75E8B95BB9748703BDA10973D7820E017C86653D59E11 EAB12A1BB1EDA330D0C1B408815ED2815CDA290D03F5BC476BA6E0E42A38EE6E 47CEC1A3AF0ADACD5573116DED106E71194260921BDB7F652E388630BDA8F40A 90B0B56A4EFA4434CE0B89A135E48B980D28223FA953049DED8C8D7E421033B9 9553A38D516B17A77E3A6ACDFC7D4DC6F1B1CE183A0E439E1660A67214ABB45B C8FCBE567B9E31200B6F2A35DECECF68FB6AFA8D4B838E963A026A0959B51F81 63C7D19BE3A67BCEC5E873AB32ECBD822C3299FD7B3BF44B440B6B7474BCA9C0 A67EAF19DA38A67482B8B38C8EAE8318B78D83AC70D6DFC20634820694020049 D4F9D65D508A0F14BB660FB9509E50C7F0D62A1EAE566B172B1311512857A099 81248F55DC2C5657C9E785955A7E9BAFA0385D41B6B5BCCE9197FCA217E9CB8A 060BADC36C5D36C7D415CF25C3180A70199A2F57C80939E709D728B3C9B08BE0 062A6E12CBB0B6F6C0491D60451226920BD09DE04CE19A13511464EA7744AFDC 390DD9C719F7307BAF72102505FECAAEEB51F00C12F1BA04E9C87D4BCD729ECB 39D0FEE94A455793EAF36BAB837072D20C058E65392A7E2EB2A3DCB4B20CFB70 6A7BE3EAAB49A6904C8CF043F8216874F53C8D2DE23248CA43223803F596DFEB 0428BAD0739E5F02A4247F35F0F441A9D7D3B3F259D4D3AF5F50899C8F716782 724DCA252F4FA386A1375A96A0A6243F0B7FD869895E120A6E787A51178BBF4D 4DCBB85BEDE1CCC62B05209E7F99F09A4559F490EA8DC0CFC28F2CFF5AD9DCA2 893E2D03081BE870A3554D3EA739C94500BDBB6D68AC10072D18192CE520F217 CA3FA25C1EF61CC550D89F60F9668CDED11DD7D26F27E7AA5492BA9DB0584070 E46A1C9AA63103C6DBAE4E76644BE7B3B36FC9814DE3071CB048ED2ADE6D7364 9333380CA233C36FE40F0F70B708658676C8E759995C5C0DC75C6083E73FF27F 1ED1160EA99FC2BB79FB1C4A2C31896B06F6A005975A2B346F9B55A40B6FAF55 EF7E0CC772C0CA2EAC4506583EFBA9981C54F335D23D2D2D6046ED64742F6BE1 BCDD4CAB96E65759586F5841C37E7B9DF5DB4C92D4552C74D769528E69B71B0B 2190B5DCFAFC2BB9B999A6F18AAD84DC09CA76BB5967818941F2106AEA0934E9 48F1C94669BEF9BD57573B92AFBF0D66E453CB0A0A68389AD6D772D200AF9BC1 1B676D1CB53C15918EBFB7BCD8B3C822BDE95C555D6190A1C932B77FC7CF6FF0 477C3F3A1343D9715947641B1CEDF9392910C0E8EC90F879E6D8C98633DA7AEE BE09060FBC0C1D4BA8CF25619B3ABBC999569B32EBD6BC3770639A1B20055FC8 3663800C9BCA939D38D5A59BB57A37E56B6D719D1FF37644C430D55AFB22C551 1878834D615ED81BE4B2FD0559A869B957741D605879880E3829E85ADD3C3F01 B9277F182403398E01366EB8586456B177FD82168A7B847C8D922B50136086CE 0E05DE8E92E336FB471A6124BAEF96437250ADF1012C6203749F24B8AE903941 70FE073CD6AC89D23168683A410BBB3187681BE44E01E3F95314FA6D67085A67 7293B4C9CD424C81160CF221CBB15500A2F5965B6BF20DC48178802C50F274B2 25F06496A9E0612D1F8B29A36BC8666DA815DB93ECB327DC3FE077CE8CCB61C3 78BA1DA7A497BBF7C6E4363E64A7454A266F1517A5A85926B35C66F54C5099C7 93B19A56D124A354050972D1B2719889D5DFB2466869041BEE1165732FF2652E 9392AB6730953128E1A20FEE50BBEEB9F92327E869969243D7A48DDE064B289C EF4F7DFCFEF679075A88574101CBA7E4EDEE8B7D333B83B6B444E3EFE0FF10FB B179CD231E227C0B35F5A72CB35C31F211C7E1042E5864DEC9AB11F3E66D357A 1D6D6B18CAFE216BA097C570C17855E4B2CE102BE87B31FD2BD5E4F4F8303EF1 468F7875052EE1CDB6BAEC1EA365C003E42DBB49AAE055C3D9D22A51F1685532 3D84137612E7F00203F7F936A9F61B92D028D0E3FE0D2FB16247D2D35D738E5B 0BC38A6D56BEE78DE97B412C60113677EE3951937EB92DCE013457FFD8EB19C8 83AAC7DF63E36A97A06593AABB0D3B44C402072E6EE60A39930627E16D7A4EB5 345FA26CB07957C0F87B9FC71C96A6CE61E124C5DD95F5F1B22E1887F080D7A7 A5B44A9535071B1EB664F591C6894952641AEB4578495BEADEC2A53643F2C086 99FE0E5F26647EFFFDAD09D5B18F4985EBF07DE4E9B6F01907F37CA7679980CA 14D3676FE568630BEDAC2FD8DE732DE8CC353754D1E44D62C059FC8EC1F1D05D 14B7C3F9F4596115E291899A76B84260141EF7D5B2C4D4434D2C6BDECFDBCF90 E4E737820C5E21A5D282165E0C1F0BD53571F6B1F3F39E8231262EC68FF050C3 A30CA548A2F6CE7A17BF78E537E31CB45859EE3AC9D4012029B554687F6655CF FE4C584D7F6F3EBBA2431334FD0D150036DB27B34C7BB9408029483574191FD6 4F2871B21D11BABFDDF800F36C7118985059F16CB5ABE49040DB820B47834A24 95274B1D62E357600D4AB7AC5C3C428EF4EBF4B78D9BF9F51CE275F383A61A31 39FBCF207DBF9CFA32EB743203460568FB1921B0B3725C3CAD15E69F7EA1B7AE 7212C216808CD4BDDD19442479513F7750630651C554E8F47D370A294C77CFE7 3A640353DCB2D0AF8ADB6DAAD1546BFF4B1885CBFC51D382B4A9ED1CBD5126E0 C50E1B2A2B6D60AC13C16E5612B94886590B051830624440C57503E44E6DFA4B 45C25C2DBE9A694C1692E6FAD663B9530F1862E74A314B17C3ABB4FD1746F0A6 C39D8BA8DD5085E4612BBE0611FACC6A5BD867E8263BFD600E28F9BE00DE141F 56B9B0C27B35E18EB10D8715F0A8418C49A424AE356C0B9827D5EF92410E4293 14759A8811D8ECEB25CCD156CCC7938E4CF6111AB91C86CB3EB6521CD4877AF9 1D1170FDDC64EF451729DE4DDE7B7D6AE2A8DA71A00D98E6F930B8083D0A8FC5 D53EDC7E7599E714DA45A5A802634F32C818D1657A513EF13928D899900CC5C2 DA3A5D46634C9CF8D38C17C39D30ECC78CF8D6A2A48B9A30F0B962C6A9386FD1 12FFABFBA9CF03AEB04921059E67CCD4F3BCF1D2EAA206DD7650D6F95E39B672 D7D71630BC411951D8D703374B9C625366D4098276807A71554D2E856E460BCC 0C877810107336F8D9A34CEB0AEA4980A19688CD21BCE52048A1DE06D000E4D6 8101BBEBA6024D66D82E6D32F66C122D33D1E8D023C9CF40734C3D17ADE8E060 8A581D759C6FA4CB07BC55F279B3E6BD6D5E105F89A6967964BB86DB2CB2215E 2538E5ADF22D06736CB0E7F61DA043D2573AF4116BAE55F53D89980791631539 92C6A91149A35FE696FA85742302436812DE6D971AF0CEE97B1F50093F338697 97DB3631A9CB43A6F8E71395B7C71C919E81EC81EE8D72359206FA407F46AFB1 BF3784D4476CD020947295CABD31A42645F7086FBBFE552C89B493A5C5D21E6C 383C18BB188E75891980AC878B1615909870BD45D5A5400069B31BC88CA3ED29 C69B63E5BD8548AB6C517576E02AA168669A1820D7F6B000B36DD4223EE64C90 0D9658C7888336C4E3082275A3622E3E6C204C4A390DA29DF3726C5CBD73698B 25B675615C596F321C0552E5961FF740A20BB6704F34848A670E2FD68C401BC6 B8D0A5F1B567E200C85D4980617BF231217BAC840D527A7E3B8B1A0C63882CBB 8B2EDE98B94A97F29B62362353359A46B7CDF77D58E9DE7336A82D35F79FBC7C F5789CB1F14D0E4F2529E965D46DAA00893D71F70142C6717C8A9F3D55C177C6 86FB6696F00B77207F27967F596383D3FA015BFD527075F89608416DC958C139 24B8BCA9F97113E5C616B7003CB544229F32B17A49C7B764F439D30539DCFA3B 476DA507EF3B0F8757224F77CDE645266ECFBBD17909338CB3A4A69F7E01B1CE D647082FDD8487800795379B8533102F1712F93FADDAE1209C2AE664916FA3C3 5D49B753EDE17A4E3EB07C2120BFECD4E43AFFDE1B9ABA29FC25F7D1FE60B770 035F431D7672D009DE7AD2D9EF4EA637108BEE2155FA29A0B5C3D91A74C8B62F 82CE4FE8BD8D3BE5CD5CDA1EEB2DC78E9B94965F3CDF4BBE7897E98B5C13927F 4C5B5706AEEE88D9DA70935EC453B8F58B4BCE893E47C076AB18662D0D21C0C9 BA1A7D9F9403420039D972A332548A0875736596AEE57768F50598E1664257AA D06D4011EA30E10BB6680287DBE8B2C287BC77ED6D78432967237C7D0F313E11 166D8094B2EB3633CC8AC002770A3CE7FAEF7FAF54E259EBD5183BF57CBC2015 75B4A34588A015EB63E914C035DDC635E75619D67A3B04A2AB41BF8C96F02840 D79604EC4ACD74FA098F52035DCA87782BCF0020F868AD1EBAF12862E0FBF607 5210539AFE92798D9727DF8ABB194E139D917C887A7932B7E5730D744E2718B4 CDE07C1D39FD85A10441A68BF1F504AEC84401CD7B11F7EC9541149EA2606E4F FEFCF843B340D2009B0BCE91E3C16120696317A6EAD3EDD16176B795E0A85F2C 8D897B848ED40B7E66C2391410CC8E2293AFBA4D1D137B4078516ECF0A8922EA EB09FD1F3F6F09BC860FC1F0EFD4670364B44F69A420D8B979651FE7ADB85A95 07BD2A83D6029E0CACB0CC5FE6328903C62D1F265148FB0F15ED319621C48D4F 364B64DD904DC8EFABA0883FF302D6CA00CBF2D6F5A07D987A4EDC17F5E5E22E A227A770B96A3E3206687D0907B292EC82779CA8E0244AA9B0A14A194649FF86 BA8B78ABB202B9C9DBB66887AF9EF9B6AED78C27B30822D3BCE6E64D5912FF1A BDE0D3AA0BEB082E3D4C8B9374F1B6D2B883C99307B85C892C0C09F3247DD211 433CB5997CD5EC17D1087790B3D7CF6C6D482CC6E5100F4EBD823CDB48A4A00B C1083BA2C3F03D3BE88E55952E9B31DC2E8B73C973DD5BEC8C6012EC430C827A D345D29299D98AFB8DB237ADA0DEBB1400F3125480855FDF7FE3F9AE8DB6916D 1CD0E1D0AA25AE647C249994FC2AC1432068132CE86553181B3B7775A6F54A8F C09A616ECF5BB6BA6DC7A46DA23573DFD7627A686B2D5CB1F372A5F097B84BC1 F5C92767B6A3E846FA4C37B6C771DF567E7F76B5A5E2BF976DD39D5537D95E93 D0637B8BFD79C0E9407534E308925FB4DAAB2265C6A81EFFF79459A55A8E8490 C2344932FE2202F913CEC0961CD70C27DE7D49E41CCE31EEAD90057A22BD31BB 373FD1495BA3068E1E96A889471683753606E1CE1AB5B7F8E5B6146EB311D436 3E25B555CB969D933EC625498EF03EBB274244D0D501411EC4C0E046C374252D 9EE823D14FA395B62DC5A93B8E8F88DDA4B5BFF74DBAEF9A559CC145242CF0B8 48B98B61D46AA3D31E2AEA36F09C290D36473A2E4308D50C6FB7FF6077999BC1 9B5BCF506B704BEA8E5991A83560827288F71292F3AC57F17755E85FD2026249 836C20466645A543A089DD11492B5B803C8812736B11391A756FB0CF1DB109D9 2B58A0092351258124ACED64A0976DDEEB3196E932E2B67CD203859DF1A3BC78 8F62FC183E0F829226DE954C767B7A49821BFCD5EA13E41C0839A2F0E1D1D552 5312C609D520C65E7DAB6F4345411810C76CA693F445F5DEC3BE5852A81BA056 E129CE74D291C691CAC791D18843AACCB5A5D1F25716D3F60B4A63B8696258B0 0CB293014AA226F07DFB7AD275BB8E69BB79F8859B433B316DCFB074308CB69E 6BD69D1C71BDE3065EB44B63A822275CEBF4007E91993EB25FEF1E7A1F4622CC 4CB0A0F978C0A323867670B023848096BEAE30B9035A7C59462E40CA974DDE2A E9133702D3CF246C2437FE704354D39D4C1774242D81CF48DCCC9D6A5D6CF8BD 08211CC0B17DC62FDCB1B2F26F2BC4B4E9B10D7542BC2B6BAD7AAD08180F2607 1D81197D099657A8F107C4114869B0E70EA98F720DF0B402CE02DEE99D6735C2 2D794A4765023B805888830F5C0162456318E8F439B2D0F869E75B9B6F6B1E00 47C3447CF716455D35937CD21BA731995FDEC1FD36DA88EA1769F7BB920005BD 897B91806932091FD91306B93CBB709B34C1E291B9A77664DD7BE84C6B716480 93853A58A7235B0CFA1FB7E2FC7480F8A79C9839C05EC25874C68DEFC4B0B884 F89564D502C8AD17ABF49718F4614E462760F661B47A3C37C5DC7BCD9FCFC897 15916FB51FDF85DC593965365E2F510EEDE0086F2C84130B9E6D9080387D8C1D 79A89C1CC56D04D8F52B03EC56FB16594C42550687B480FD935632C9A00FB4A6 AA2C83CD5B1D5E3A300CABE3A38B94723A85E42A78FD28EF9126858CFE6A2BD7 6B9D30ECBE428E92002A046C136D9EDED1B74D79E77A3ADCB299CB98117B16C8 432888FA7DC97E6F9CAE1056302B9B966587CEBAFA9028B982D0424019B27D05 30 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR10 %!PS-AdobeFont-1.1: CMR10 1.00B %%CreationDate: 1992 Feb 19 19:54:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 1 /Delta put dup 3 /Lambda put dup 10 /Omega put dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 19 /acute put dup 22 /macron put dup 34 /quotedblright put dup 35 /numbersign put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 61 /equal put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 89 /Y put dup 90 /Z put dup 91 /bracketleft put dup 92 /quotedblleft put dup 93 /bracketright put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 123 /endash put dup 127 /dieresis put readonly def /FontBBox{-251 -250 1009 969}readonly def /UniqueID 5000793 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMBX12 %!PS-AdobeFont-1.1: CMBX12 1.0 %%CreationDate: 1991 Aug 20 16:34:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /ff put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 65 /A put dup 69 /E put dup 73 /I put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 121 /y put readonly def /FontBBox{-53 -251 1139 750}readonly def /UniqueID 5000769 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR9 %!PS-AdobeFont-1.1: CMR9 1.0 %%CreationDate: 1991 Aug 20 16:39:59 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /ff put dup 40 /parenleft put dup 41 /parenright put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 73 /I put dup 79 /O put dup 87 /W put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{-39 -250 1036 750}readonly def /UniqueID 5000792 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMBX9 %!PS-AdobeFont-1.1: CMBX9 1.0 %%CreationDate: 1991 Aug 20 16:36:25 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 65 /A put dup 97 /a put dup 98 /b put dup 99 /c put dup 114 /r put dup 115 /s put dup 116 /t put readonly def /FontBBox{-58 -250 1195 750}readonly def /UniqueID 5000767 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMTT12 %!PS-AdobeFont-1.1: CMTT12 1.0 %%CreationDate: 1991 Aug 20 16:45:46 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTT12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch true def end readonly def /FontName /CMTT12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 45 /hyphen put dup 46 /period put dup 64 /at put dup 99 /c put dup 101 /e put dup 102 /f put dup 105 /i put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 114 /r put dup 115 /s put dup 117 /u put dup 118 /v put readonly def /FontBBox{-1 -234 524 695}readonly def /UniqueID 5000833 def currentdict end currentfile eexec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cleartomark %%EndFont TeXDict begin 39158280 55380996 1000 600 600 (prewetting1.dvi) @start /Fa 254[159 1[{}1 206.559 /CMR17 rf /Fb 135[115 5[91 4[177 60 9[86 31[154 52[105 13[{}7 206.559 /CMMI12 rf /Fc 245[115 10[{}1 172.188 /CMR17 rf /Fd 154[34 101[{}1 58.1154 /CMBX7 rf /Fe 178[113 77[{}1 119.552 /CMMI12 rf /Ff 158[89 97[{}1 172.188 /CMMI12 rf /Fg 203[59 1[59 59 59 48[{}4 119.552 /CMR12 rf /Fh 173[146 82[{}1 172.188 /CMSY10 rf /Fi 157[65 98[{}1 83.022 /MSAM10 rf /Fj 134[44 44 2[46 32 33 33 44 46 42 46 1[23 2[23 46 42 25 37 46 37 1[42 26[54 25[23 44[{}21 83.022 /CMSL10 rf /Fk 154[38 20[70 80[{}2 58.1154 /TeX-cmex7 rf /Fl 169[41 86[{}1 58.1154 /CMSS8 rf /Fm 140[23 9[17 5[25 5[17 1[17 38[28 28 28 28 28 4[43 1[22 22 36[38 3[{}14 41.511 /CMR5 rf /Fn 149[19 33[50 21[39 1[18 23[45 20[31 2[45{}7 41.511 /CMSY5 rf /Fo 134[40 39 55 38 45 28 34 35 38 42 42 47 68 21 38 25 25 42 38 25 38 42 38 38 42 3[25 1[25 3[83 2[59 47 61 1[56 64 62 74 52 1[44 32 1[64 54 1[63 59 58 62 6[25 42 3[42 1[42 42 42 42 1[25 30 25 2[34 34 27[47 12[{}57 83.022 /CMTI10 rf /Fp 134[50 1[69 1[53 37 38 39 1[53 48 53 80 27 50 29 27 53 48 29 44 53 42 53 46 3[27 1[27 6[66 1[72 1[65 3[57 8[69 1[72 7[48 2[48 48 48 48 48 48 2[27 1[27 2[37 37 40[{}41 83.022 /CMBX10 rf /Fq 165[55 6[46 60 1[51 1[60 8[55 69[{}6 83.022 /MSBM10 rf /Fr 134[33 33 1[33 34 24 24 24 1[34 31 34 51 17 2[17 2[19 27 34 27 1[31 22[32 4[42 9[17 7[31 31 1[31 3[17 31[34 12[{}26 58.1154 /CMSL8 rf /Fs 165[39 90[{}1 58.1154 /MSBM7 rf /Ft 168[78 55 57 17[53 67[{}4 83.022 /CMSS10 rf /Fu 134[30 33 3[23 1[28 3[37 51 20 31 1[22 34 2[28 31 27 2[25 13[43 3[45 12[43 3[31 1[19 19 28[33 5[30 1[35 5[25 2[33 12[{}25 41.511 /CMMI5 rf /Fv 145[34 3[20 27 27 34 34 9[45 45 7[41 57 9[57 2[36 1[36 1[53 5[34 4[0 1[59 1[45 66 19 9[66 1[66 1[34 66 6[52 1[52 2[52 52 13[52 2[34 1[20 52{}32 58.1154 /CMSY7 rf /Fw 143[83 55 55 8[46 10[46 106 120 4[69 1[78 88 17[74 74 74 74 74 74 74 14[67 67 4[48 48 66 66 4[62 62 6[61 61 50 50 3[28 2[48 48 6[38 38{}34 83.022 /CMEX10 rf /Fx 135[35 3[26 26 3[33 37 55 19 2[19 1[33 2[37 30 37 33 3[19 1[19 40 28[51 2[19 33 33 1[33 1[33 33 33 33 33 1[19 2[51 1[26 26 17[33 11[47 6[45 1[55 1[{}34 58.1154 /CMR7 rf /Fy 142[62 2[42 2[42 23 32 32 42 42 7[55 1[55 55 3[82 3[50 70 9[70 2[44 1[44 1[66 5[42 1[46 46 1[0 3[55 83 10[83 1[83 2[83 4[83 65 65 1[65 65 1[65 65 2[65 1[42 4[65 3[65 3[65 23 65{}41 83.022 /CMSY10 rf /Fz 133[32 34 38 48 33 39 25 31 31 2[33 41 59 21 35 27 23 39 2[31 35 30 29 36 28 7[54 5[50 3[53 63 46 56 37 1[54 2[49 1[48 50 50 35 1[52 34 52 20 20 23[31 4[37 31 38 34 2[33 1[39 39 2[34 30 28 1[35 38 12[{}54 58.1154 /CMMI7 rf /FA 133[39 41 47 59 40 48 30 39 37 37 2[50 1[25 43 34 29 48 1[41 39 43 36 36 44 35 5[57 48 69 1[48 1[49 1[63 3[67 81 57 71 46 1[69 1[53 61 1[59 63 62 44 1[65 42 65 23 23 27[49 45 36 47 43 2[41 50 48 48 2[41 36 34 37 43 47 53 11[{}62 83.022 /CMMI10 rf /FB 128[42 3[42 37 44 44 60 44 46 32 33 33 44 46 42 46 69 23 44 25 23 46 42 25 37 46 37 46 42 3[23 42 23 51 62 1[85 62 62 60 46 61 65 57 65 62 76 52 65 43 30 62 65 54 57 63 60 59 62 3[65 1[23 23 42 42 42 42 42 42 42 42 42 42 1[23 28 23 65 1[32 32 23 3[69 42 11[42 2[42 4[69 46 46 48 60 6[58 1[69 1[{}87 83.022 /CMR10 rf /FC 134[59 1[81 59 62 44 44 46 2[56 62 93 31 2[31 62 56 34 51 62 50 62 54 12[78 62 2[77 6[42 3[74 15[56 56 56 56 56 2[31 37 31 32[65 11[{}34 99.6264 /CMBX12 rf /FD 138[75 52 53 55 2[67 75 112 37 2[37 2[41 61 75 60 1[65 13[75 100 1[92 6[50 7[102 14[67 67 49[{}21 119.552 /CMBX12 rf /FE 133[34 41 41 55 41 43 30 30 30 1[43 38 43 64 21 41 1[21 43 38 23 34 43 34 43 38 9[79 7[60 5[28 26[21 26 21 2[30 30 28[45 11[{}33 74.7198 /CMR9 rf /FF 139[34 35 36 14[39 49 43 31[67 65[{}7 74.7198 /CMBX9 rf /FG 137[51 51 1[51 51 3[51 51 51 51 1[51 2[51 51 1[51 34[51 17[51 51 45[{}15 99.6264 /CMTT12 rf /FH 134[51 2[51 54 38 38 38 1[54 49 54 1[27 51 1[27 1[49 1[43 54 43 54 49 7[73 2[73 73 70 54 72 1[66 1[73 89 61 1[50 35 2[64 2[70 1[73 10[49 2[49 49 1[49 1[27 33 27 4[27 19[49 19[{}42 99.6264 /CMR12 rf /FI 135[70 2[73 51 52 51 1[73 66 73 1[36 2[36 2[40 58 73 58 1[66 27[90 56[72 12[{}17 143.462 /CMR17 rf end %%EndProlog %%BeginSetup %%Feature: *Resolution 600dpi TeXDict begin %%PaperSize: A4 end %%EndSetup %%Page: 1 1 TeXDict begin 1 0 bop Black Black Black Black 568 872 a FI(En)l(tropic)44 b(repulsion)f(of)g(an)g(in)l(terface)g(in)h(an)f (external)1827 1054 y(\014eld)1741 1295 y FH(Y.V)-8 b(elenik)952 1411 y(Lab)s(oratoire)32 b(d'Analyse,)i(T)-8 b(op)s(ologie,)33 b(Probabilit)m(\023)-46 b(es)1565 1528 y(UMR-CNRS)33 b(6632)1290 1644 y(C.M.I.,)h(Univ)m(ersit)m(\023)-46 b(e)35 b(de)e(Pro)m(v)m(ence)1584 1760 y(Marseille,)h(F)-8 b(rance)1357 1876 y FG(velenik@cmi.univ-mrs.fr)1687 2072 y FH(July)34 b(3,)e(2003)p Black Black 1778 2352 a FF(Abstract)p Black Black 837 2463 a FE(W)-6 b(e)21 b(consider)h(an)f(in)n(terface)h (ab)r(o)n(v)n(e)f(an)g(attractiv)n(e)h(hard)f(w)n(all)h(in)f(the)g (complete)722 2555 y(w)n(etting)e(regime,)j(and)c(submitted)g(to)g(the) g(action)i(of)f(an)f(external)h(increasing,)j(con-)722 2646 y(v)n(ex)d(p)r(oten)n(tial,)j(and)d(study)g(its)h(delo)r (calization)j(as)d(the)f(in)n(tensit)n(y)g(of)i(this)f(p)r(oten)n(tial) 722 2737 y(v)l(anishes.)33 b(Our)18 b(main)i(motiv)l(ation)g(is)g(the)f (analysis)h(of)g(critical)h(prew)n(etting,)g(whic)n(h)722 2829 y(corresp)r(onds)27 b(to)f(the)f(c)n(hoice)h(of)h(a)f(linear)g (external)g(p)r(oten)n(tial.)837 2920 y(W)-6 b(e)21 b(also)h(presen)n (t)e(partial)i(results)g(on)e(critical)j(prew)n(etting)e(in)f(the)h(t)n (w)n(o)g(dimen-)722 3011 y(sional)29 b(Ising)e(mo)r(del,)h(as)f(w)n (ell)h(as)g(a)f(few)h(\(w)n(eak\))f(results)h(on)f(path)n(wise)g (estimates)722 3103 y(for)g(the)e(pure)g(w)n(etting)h(problem)g(for)h (e\013ectiv)n(e)e(in)n(terface)i(mo)r(dels.)515 3374 y FD(1)134 b(In)l(tro)t(duction)45 b(and)g(results)515 3572 y FC(1.1)112 b(E\013ectiv)m(e)37 b(in)m(terface)h(mo)s(dels)515 3726 y FB(There)29 b(has)g(b)r(een)h(a)f(lot)g(of)h(in)n(terest)f (recen)n(tly)g(in)g(the)h(prop)r(erties)f(of)g(e\013ectiv)n(e)h(in)n (terface)515 3825 y(mo)r(dels)i(in)i(the)f(presence)f(of)h(an)f (attractiv)n(e)g(hard)g(w)n(all,)i(and)e(the)i(asso)r(ciated)d(w)n (etting)515 3925 y(phase)h(transition)h([7)o(,)g(12)o(,)h(24)o(],)g(as) f(w)n(ell)g(as)f(the)i(related)e(problems)g(of)h(en)n(tropic)g(repul-) 515 4024 y(sion)27 b([9)o(,)h(6,)f(14)o(,)h(5,)f(15)o(,)h(16)o(,)g(3)o (,)g(2])f(and)h(pinning)g(b)n(y)f(a)g(lo)r(cal)g(p)r(oten)n(tial)h([20) o(,)g(4)o(,)g(17)o(,)g(23)o(,)f(8].)639 4124 y(In)38 b(the)h(presen)n(t)e(w)n(ork,)i(w)n(e)e(consider)g FA(d)p FB(-dimensional)g(e\013ectiv)n(e)h(in)n(terface)f(mo)r(dels)515 4224 y(with)32 b(con)n(v)n(ex)e(in)n(teractions.)47 b(That)31 b(is,)i(the)f(in)n(terface)e(is)i(describ)r(ed)f(b)n(y)g(a)g (collection)g(of)515 4323 y(non-negativ)n(e)20 b(real)i(n)n(um)n(b)r (ers)g FA(X)1554 4335 y Fz(i)1581 4323 y FB(,)i FA(i)f Fy(2)g FB(\003)1816 4335 y Fz(N)1902 4323 y FB(=)f Fy(f\000)p FA(N)t(;)14 b(:)g(:)g(:)f(;)h(N)9 b Fy(g)2469 4293 y Fz(d)2507 4323 y FB(,)24 b(represen)n(ting)c(the)j(heigh)n(t)515 4423 y(of)k(the)h(in)n(terface)f(ab)r(o)n(v)n(e)f(site)i FA(i)p FB(.)37 b(The)27 b(probabilit)n(y)g(measure)f(is)i(giv)n(en)f(b) n(y)598 4632 y(P)655 4644 y Fz(N)s(;)p Fx(+)p Fz(;\025;\035)902 4632 y FB(\(d)p FA(X)7 b FB(\))23 b(=)1199 4565 y Fw(\000)1237 4632 y FA(Z)1294 4644 y Fz(N)s(;)p Fx(+)p Fz(;\025;\035)1541 4565 y Fw(\001)1579 4582 y Fv(\000)p Fx(1)1696 4632 y FB(exp)1823 4540 y Fw(n)1878 4632 y Fy(\000)2075 4553 y Fw(X)1957 4735 y Fv(h)p Fz(i;j)s Fv(i\\)p Fx(\003)2174 4743 y Fu(N)2228 4735 y Fv(6)p Fx(=)p Fv(;)2299 4632 y Ft(U)p FB(\()p FA(X)2457 4644 y Fz(i)2503 4632 y Fy(\000)18 b FA(X)2655 4644 y Fz(j)2690 4632 y FB(\))h Fy(\000)2847 4553 y Fw(X)2824 4731 y Fz(i)p Fv(2)p Fx(\003)2937 4739 y Fu(N)3005 4632 y FA(\025)14 b Ft(V)q FB(\()p FA(X)3224 4644 y Fz(i)3252 4632 y FB(\))3284 4540 y Fw(o)1603 4878 y Fy(\002)1717 4800 y Fw(Y)1686 4978 y Fz(i)p Fv(2)p Fx(\003)1799 4986 y Fu(N)1867 4878 y FB(\(d)p FA(X)2014 4890 y Fz(i)2060 4878 y FB(+)k FA(\035)s(\016)2228 4890 y Fx(0)2265 4878 y FB(\(d)p FA(X)2412 4890 y Fz(i)2440 4878 y FB(\)\))2603 4800 y Fw(Y)2519 4983 y Fz(i)p Fv(2)p Fs(Z)2626 4967 y Fu(d)2661 4983 y Fv(n)p Fx(\003)2740 4991 y Fu(N)2807 4878 y FA(\016)2844 4890 y Fx(0)2881 4878 y FB(\(d)p FA(X)3028 4890 y Fz(i)3056 4878 y FB(\))c FA(;)83 b FB(\(1.1\))p Black 1926 5255 a(1)p Black eop end %%Page: 2 2 TeXDict begin 2 1 bop Black 515 232 a Fr(En)n(tropic)22 b(repulsion)g(in)f(external)h(\014eld;)g(v)n(ersion)f(from)g(July)g(3,) f(2003)1159 b FB(2)p Black 515 523 a(where)36 b FA(\016)801 535 y Fx(0)874 523 y FB(is)h(the)f(Dirac)g(mass)g(at)g(0,)i FA(\025)f FB(is)g(a)f(strictly)g(p)r(ositiv)n(e)g(real)f(n)n(um)n(b)r (er,)k FA(\035)h Fy(\025)d FB(0)515 623 y(and)g(the)h(function)h Ft(U)f FB(satis\014es)f FA(c)i(<)h Ft(U)1823 593 y Fv(00)1905 623 y FA(<)g FB(1)p FA(=c)d FB(for)g(some)g FA(c)j(>)g FB(0.)67 b(W)-7 b(e)38 b(are)e(mostly)515 722 y(in)n(terested)27 b(in)g(the)h(case)e Ft(V)q FB(\()p FA(x)p FB(\))f(=)d Fy(j)p FA(x)p Fy(j)p FB(,)28 b(but)g(w)n(e)f(allo)n(w)f(for)h(general)f Ft(V)e FB(:)f Fq(R)2819 692 y Fx(+)2898 722 y Fy(!)g Fq(R)3064 692 y Fx(+)3119 722 y FB(,)k(whic)n(h)515 822 y(are)22 b(con)n(v)n(ex,)h(increasing,)g(and)h(satisfy)f Ft(V)q FB(\(0\))h(=)f(0)g(and)g(the)h(follo)n(wing)f(gro)n(wth)f (condition:)515 922 y(There)27 b(exists)g FA(f)32 b FB(:)23 b Fq(R)1163 891 y Fx(+)1241 922 y Fy(!)g Fq(R)1407 891 y Fx(+)1490 922 y FB(suc)n(h)k(that,)h(for)f(all)g FA(\013)d(>)e FB(0,)1432 1142 y(lim)14 b(sup)1474 1208 y Fz(x)p Fv(!1)1710 1085 y FA(V)19 b FB(\()p FA(\013x)p FB(\))p 1710 1122 233 4 v 1737 1199 a FA(V)g FB(\()p FA(x)p FB(\))1976 1142 y Fy(\024)j FA(f)9 b FB(\()p FA(\013)p FB(\))24 b FA(<)e Fy(1)14 b FA(:)515 1367 y FB(\(Ob)n(viously)23 b(an)n(y)g(con)n(v)n(ex)f(p)r(olynomial)i(is)g(\014ne.\))36 b(The)24 b(parameter)f FA(\035)k FB(corresp)r(onds)22 b(to)i(the)515 1467 y(strength)j(of)g(the)h(pinning)g(p)r(oten)n(tial)g (lo)r(cally)f(attracting)f(the)i(in)n(terface)f(to)h(the)g(w)n(all.)p Black 515 1628 a Fp(Remark)k(1)p Black 41 w Fo(Our)25 b(r)l(esults)g(and)h(pr)l(o)l(ofs)h(c)l(an)e(b)l(e)h(extende)l(d)g(str) l(aightforwar)l(d)t(ly)i(to)e(the)f(c)l(ase)515 1728 y(of)30 b(a)g(squar)l(e-wel)t(l)h(p)l(otential)f(of)h(the)f(form)g Fy(\000)p FA(b)p Fp(1)2036 1740 y Fz(X)2090 1748 y Fu(i)2116 1740 y Fv(\024)p Fz(a)2208 1728 y Fo(,)g FA(b)23 b Fy(\025)g FB(0)p Fo(,)29 b FA(a)23 b(>)g FB(0)p Fo(.)515 1889 y FB(When)33 b(the)g(pinning)h(p)r(oten)n(tial)e(is)h(absen)n(t)g(\(i.e.) 53 b FA(\035)35 b FB(=)c(0\),)j(w)n(e)f(simply)g(omit)g(the)g(corre-) 515 1989 y(sp)r(onding)21 b(subscript.)34 b(W)-7 b(e)21 b(denote)g(b)n(y)g FA(\035)1799 2001 y Fx(c)1854 1989 y FB(the)g(critical)g(v)-5 b(alue)21 b(of)g(the)g(pinning)g(parameter,) 1090 2211 y FA(\035)1135 2223 y Fx(c)1191 2211 y FB(=)i(sup)1418 2093 y Fw(\032)1480 2211 y FA(\035)40 b FB(:)75 b(lim)1625 2264 y Fz(N)6 b Fv(!1)1830 2211 y Fy(j)p FB(\003)1911 2223 y Fz(N)1974 2211 y Fy(j)1997 2176 y Fv(\000)p Fx(1)2100 2211 y FB(log)2231 2154 y FA(Z)2288 2166 y Fz(N)s(;)p Fx(+)p Fz(;)p Fx(0)p Fz(;\035)p 2231 2191 299 4 v 2260 2267 a FA(Z)2317 2279 y Fz(N)s(;)p Fx(+)p Fz(;)p Fx(0)2562 2211 y FB(=)22 b(0)2691 2093 y Fw(\033)2781 2211 y FA(:)404 b FB(\(1.2\))515 2434 y(This)33 b(corresp)r(onds)f(to)i(the)g(v)-5 b(alue)34 b(of)f(the)i(pinning)e(parameter)g(at)g(whic)n(h)h(the)g(w)n (etting)515 2534 y(transition)f(tak)n(es)g(place.)56 b(In)34 b(the)g(case)f Ft(U)p FB(\()p FA(x)p FB(\))i(=)e FA(x)2172 2504 y Fx(2)2210 2534 y FB(,)j(it)e(is)g(kno)n(wn)f(that)i FA(\035)2949 2546 y Fx(c)3016 2534 y FA(>)e FB(0)h(when)515 2634 y FA(d)c Fy(\024)f FB(2)i([12)o(],)i(while)f FA(\035)1206 2646 y Fx(c)1269 2634 y FB(=)d(0)i(when)h FA(d)e Fy(\025)f FB(3)j([7)o(].)49 b(\(The)32 b(situation)g(is)f(di\013eren)n(t)h(when)f (one)515 2733 y(drops)e(the)h(assumption)f(of)h(strict)f(con)n(v)n (exit)n(y)f(of)i Ft(U)p FB(,)g(see)g([12)o(].\))43 b(W)-7 b(e)31 b(write)e Ft(CW)f FB(=)e Fy(f)p FA(\035)j Fy(\025)515 2833 y FB(0)38 b(:)h FA(\035)28 b(<)c(\035)864 2845 y Fz(c)898 2833 y Fy(g)19 b([)g(f)p FB(0)p Fy(g)27 b FB(to)i(denote)g (the)g(region)e(of)i(complete)g(w)n(etting;)g(for)f(these)h(v)-5 b(alues)28 b(of)515 2932 y(the)g(pinning)g(parameter,)e(the)i(in)n (terface)f(is)g(delo)r(calized)g(when)h FA(\025)23 b FB(=)g(0.)639 3032 y(Let)35 b Fy(H)865 3044 y Fz(\025;d)997 3032 y FB(b)r(e)g(de\014ned)g(as)e(follo)n(ws:)50 b(In)34 b(dimension)h FA(d)f FB(=)g(2,)i Fy(H)q FB(\()p FA(\025)p FB(;)14 b(2\))35 b(=)e Fy(j)14 b FB(log)g FA(\025)p Fy(j)p FB(;)39 b(in)515 3132 y(dimensions)27 b FA(d)c Fy(\025)g FB(3,)k Fy(H)1256 3144 y Fz(\025;d)1377 3132 y FB(=)c Fy(j)14 b FB(log)g FA(\025)p Fy(j)1694 3102 y Fx(1)p Fz(=)p Fx(2)1799 3132 y FB(.)37 b(Then)27 b(our)g(main)h(result)f(can)g (b)r(e)h(stated)g(as)p Black 515 3293 a Fp(Theorem)j(1)p Black 41 w Fo(L)l(et)37 b FA(\035)i Fy(2)e Ft(CW)r Fo(.)61 b(Ther)l(e)38 b(exist)e(dimension-dep)l(endent,)41 b(strictly)d(p)l (ositive)515 3393 y(c)l(onstants)29 b FA(\016)s Fo(,)h FA(\025)1023 3405 y Fx(0)1061 3393 y Fo(,)g FA(r)r Fo(,)h(and)f FA(c)g Fo(such)f(that:)39 b(F)-6 b(or)30 b(al)t(l)h FA(\025)23 b(<)g(\025)2311 3405 y Fx(0)2378 3393 y Fo(and)31 b FA(N)g(>)23 b(\025)2774 3363 y Fv(\000)p Fz(r)2863 3393 y Fo(,)600 3581 y FB(P)657 3593 y Fz(N)s(;)p Fx(+)p Fz(;\025;\035)904 3514 y Fw(\000)942 3581 y Fy(j)p FB(\003)1023 3593 y Fz(N)1086 3581 y Fy(j)1109 3547 y Fv(\000)p Fx(1)1235 3503 y Fw(X)1212 3681 y Fz(i)p Fv(2)p Fx(\003)1325 3689 y Fu(N)1393 3581 y FA(X)1462 3593 y Fz(i)1512 3581 y Fy(62)g FB(\()p FA(\016)s Fy(H)1732 3593 y Fz(\025;d)1831 3581 y FA(;)14 b(\016)1908 3547 y Fv(\000)p Fx(1)1997 3581 y Fy(H)2067 3593 y Fz(\025;d)2165 3581 y FB(\))2197 3514 y Fw(\001)2258 3581 y Fy(\024)23 b FB(exp)13 b Fy(f\000)p FA(c)h(\025)g Ft(V)h FB(\()p Fy(H)2877 3593 y Fz(\025;d)2975 3581 y FB(\))28 b Fy(j)p FB(\003)3116 3593 y Fz(N)3179 3581 y Fy(jg)f FA(:)515 3840 y Fo(A)l(ctual)t(ly,)j(the)g(upp)l(er)g(b) l(ound)g(c)l(an)g(b)l(e)f(str)l(engthene)l(d)h(as)521 4029 y FB(P)578 4041 y Fz(N)s(;)p Fx(+)p Fz(;\025;\035)826 3962 y Fw(\000)864 4029 y Fy(j)p FB(\003)945 4041 y Fz(N)1007 4029 y Fy(j)1030 3995 y Fv(\000)p Fx(1)1157 3950 y Fw(X)1133 4128 y Fz(i)p Fv(2)p Fx(\003)1246 4136 y Fu(N)1314 4029 y FA(X)1383 4041 y Fz(i)1434 4029 y Fy(62)23 b FB(\()p FA(\016)s Fy(H)1654 4041 y Fz(\025;d)1752 4029 y FA(;)14 b(\016)1829 3995 y Fv(\000)p Fx(1)1918 4029 y Fy(H)1988 4041 y Fz(\025;d)2086 4029 y FB(\))2118 3962 y Fw(\001)2180 4029 y Fy(\024)22 b FB(exp)2408 3962 y Fw(\010)2456 4029 y Fy(\000)p FA(c)14 b(\016)2611 3995 y Fv(\000)p Fx(1)2714 4029 y FA(\025)g Ft(V)h FB(\()q Fy(H)2949 4041 y Fz(\025;d)3047 4029 y FB(\))28 b Fy(j)p FB(\003)3188 4041 y Fz(N)3250 4029 y Fy(j)3273 3962 y Fw(\011)3349 4029 y FA(:)p Black 515 4288 a Fp(Remark)k(2)p Black 41 w Fo(We)26 b(do)i(not)e(state)g (and)h(pr)l(ove)h(her)l(e)f(the)f(c)l(orr)l(esp)l(onding)i(r)l(esults)e (in)h(dimen-)515 4388 y(sion)g FB(1)p Fo(.)38 b(The)28 b(r)l(e)l(ason)f(is)h(that,)g(in)f(that)g(c)l(ase,)i(much)e(mor)l(e)h (detaile)l(d)h(informations,)g(valid)515 4487 y(for)c(an)g(immensely)g (lar)l(ger)h(class)f(of)g(inter)l(actions)g Ft(U)g Fo(c)l(an)f(b)l(e)h (obtaine)l(d.)38 b(This)26 b(is)f(of)g(inter-)515 4587 y(est,)i(sinc)l(e)g(one)f(would)h(like)h(to)e(understand)h(the)f(de)l (gr)l(e)l(e)h(of)g(universality)h(in)e(the)h(b)l(ehavior)515 4687 y(found)32 b(her)l(e.)44 b(These)33 b(r)l(esults)e(wil)t(l)h(app)l (e)l(ar)h(elsewher)l(e)g([22)r(].)44 b(L)l(et)31 b(us)g(just)g(mention) h(that,)515 4786 y(when)d FA(d)23 b FB(=)g(1)p Fo(,)29 b(the)g(interfac)l(e)g(is)g(r)l(ep)l(el)t(le)l(d)h(to)f(a)g(height)h (of)g(or)l(der)f Fy(H)q Fo(,)g(the)g(unique)g(solution)515 4886 y(of)h(the)g(e)l(quation)1657 4985 y FA(\025)p Fy(H)1776 4951 y Fx(2)1814 4985 y Ft(V)q FB(\(2)p Fy(H)q FB(\))23 b(=)g(1)14 b FA(:)p Black Black eop end %%Page: 3 3 TeXDict begin 3 2 bop Black 515 232 a Fr(En)n(tropic)22 b(repulsion)g(in)f(external)h(\014eld;)g(v)n(ersion)f(from)g(July)g(3,) f(2003)1159 b FB(3)p Black 515 523 a(The)29 b(previous)f(theorem)g (only)g(yields)h(estimates)g(on)f(the)i(heigh)n(t)e(of)h(the)h(\014eld) f(a)n(v)n(eraged)515 623 y(o)n(v)n(er)39 b(the)h(b)r(o)n(x.)76 b(It)41 b(is)f(ho)n(w)n(ev)n(er)f(v)n(ery)g(easy)h(to)g(deriv)n(e)g (from)g(it)h(the)g(follo)n(wing)f(lo)r(cal)515 722 y(estimates.)p Black 515 873 a Fp(Corollary)31 b(1)p Black 42 w Fo(L)l(et)26 b FA(\035)g Fy(2)d(C)5 b(W)33 b Fo(and)27 b(\014x)f FB(0)d FA(<)f(\017)h(<)g FB(1)p Fo(.)37 b(Ther)l(e)27 b(exist)g FA(\016)f(>)c FB(0)k Fo(and)h FA(\025)3003 885 y Fx(0)3064 873 y FA(>)c FB(0)j Fo(such)515 973 y(that,)k(for)h(al)t(l)f FA(\025)24 b(<)e(\025)1168 985 y Fx(0)1236 973 y Fo(and)30 b FA(N)i(>)23 b(N)1651 985 y Fx(0)1687 973 y FB(\()p FA(\025)p FB(\))p Fo(,)1347 1136 y FB(sup)1326 1206 y Fz(i)p Fv(2)p Fx(\003)1439 1214 y Fu(N)1507 1136 y FB(E)1564 1148 y Fz(N)s(;)p Fx(+)p Fz(;\025;\035)1812 1136 y FB(\()p FA(X)1913 1148 y Fz(i)1940 1136 y FB(\))h Fy(\024)e FA(\016)2123 1102 y Fv(\000)p Fx(1)2212 1136 y Fy(j)14 b FB(log)g FA(\025)p Fy(j)2441 1102 y Fz(\027)t Fx(\()p Fz(d)p Fx(\))2570 1136 y FA(;)1347 1334 y FB(inf)1301 1387 y Fz(i)p Fv(2)p Fx(\003)1414 1395 y Fu(\017N)1507 1334 y FB(E)1564 1346 y Fz(N)s(;)p Fx(+)p Fz(;\025;\035)1812 1334 y FB(\()p FA(X)1913 1346 y Fz(i)1940 1334 y FB(\))24 b Fy(\025)e FA(\016)17 b Fy(j)d FB(log)g FA(\025)p Fy(j)2366 1300 y Fz(\027)t Fx(\()p Fz(d)p Fx(\))2508 1334 y FB(;)639 1618 y(Our)28 b(main)g(motiv)-5 b(ation)29 b(for)e(studying)i(this)f (mo)r(del)h(comes)f(from)g(the)h(ph)n(ysical)e(phe-)515 1718 y(nomenon)d(of)g Fo(critic)l(al)k(pr)l(ewetting)p FB(.)36 b(Consider)23 b(some)h(substance)g(in)g(the)h(regime)e(of)i (phase)515 1818 y(co)r(existence;)e(let)g(us)f(call)g(the)h(t)n(w)n(o)e (equilibrium)i(phases)e FA(A)i FB(and)f FA(B)t FB(.)36 b(Supp)r(ose)22 b(that)h(phase)515 1917 y FA(A)j FB(o)r(ccupies)g(the)h (bulk)f(of)g(the)h(v)n(essel,)e(while)i(the)f(b)r(oundary)g(of)g(the)h (latter)e(fa)n(v)n(ors)g(phase)515 2017 y FA(B)t FB(.)37 b(As)27 b(a)g(result,)g(a)g(\014lm)g(of)g FA(B)32 b FB(phase)26 b(is)h(generated)f(along)g(the)i(w)n(alls.)36 b(It)27 b(is)g(w)n(ell-kno)n(wn)515 2117 y(that)34 b(b)n(y)g(increasing)e(the)j (temp)r(erature,)g(the)g(system)e(ma)n(y)h(undergo)f(a)g(surface)h (phase)515 2216 y(transition,)c(the)h(w)n(etting)f(transition,)h (re\015ected)f(in)h(the)g(b)r(eha)n(vior)e(of)h(this)h(\014lm:)43 b(Belo)n(w)515 2316 y(the)c(w)n(etting)g(temp)r(erature)g(the)h(\014lm) f(has)g(a)g(microscopic)e(width)j(\(partial)f(w)n(etting\),)515 2415 y(while)29 b(ab)r(o)n(v)n(e)f(it)i(its)g(width)g(b)r(ecomes)f (macroscopic)e(\(complete)j(w)n(etting\),)g(in)g(the)g(sense)515 2515 y(that)e(it)g(div)n(erges)e(in)h(the)h(thermo)r(dynamic)g(limit.) 639 2615 y(Supp)r(ose)e(no)n(w)e(that,)j(starting)d(from)h(the)h (complete)f(w)n(etting)g(regime,)g(the)h(system)f(is)515 2714 y(pulled)k(a)n(w)n(a)n(y)e(from)i(phase)f(co)r(existence)h(and)f (only)h(phase)f FA(A)i FB(remains)e(thermo)r(dynami-)515 2814 y(cally)i(stable.)46 b(The)31 b(\014lm)g(of)g(\(no)n(w)f (unstable\))h FA(B)k FB(phase,)c(though)g(still)g(presen)n(t,)g(cannot) 515 2914 y(o)r(ccup)n(y)d(a)g(macroscopic)e(region)h(and)h(therefore)g (its)g(width)h(sta)n(ys)e(microscopic)g(\(i.e.)40 b(re-)515 3013 y(mains)34 b(\014nite)g(in)g(the)h(thermo)r(dynamic)f(limit\).)57 b(Critical)34 b(prew)n(etting)f(corresp)r(onds)f(to)515 3113 y(the)27 b(\(con)n(tin)n(uous\))f(div)n(ergence)g(of)h(the)g (\014lm)g(thic)n(kness)g(as)f(the)h(system)g(nears)e(the)j(phase)515 3212 y(co)r(existence)20 b(manifold.)35 b(If)22 b(w)n(e)e(denote)h(b)n (y)g FA(\025)h FB(the)g(free)e(energy)g(di\013erence)h(b)r(et)n(w)n (een)h(phase)515 3312 y FA(B)30 b FB(and)25 b(phase)g FA(A)p FB(,)h(then)g(one)g(is)f(in)n(terested)g(in)h(the)g(b)r(eha)n (vior)e(of)i(the)g(a)n(v)n(erage)c(\014lm)k(width)515 3412 y(as)h(a)g(function)h(of)g FA(\025)p FB(.)639 3511 y(The)19 b(Gibbs)f(measures)f(\(1.1\))i(pro)n(vide)e(a)h(natural)f(mo)r (delization)h(of)h(this)f(phenomenon.)515 3611 y(Indeed,)31 b(when)g(the)g(external)f(p)r(oten)n(tial)h(is)g(c)n(hosen)e(as)h Ft(V)q FB(\()p FA(x)p FB(\))g(=)e FA(x)p FB(,)k(these)f(measures)e(in-) 515 3711 y(tro)r(duce)36 b(a)f(p)r(enalization)h(of)g(the)g(form)g(\\)p FA(\025)p Fy(\002)g FB(the)g(v)n(olume)g(of)g(the)g(w)n(et)g(la)n(y)n (er",)g(whic)n(h)515 3810 y(corresp)r(ond)24 b(to)j(the)f(free)g (energetic)g(cost)f(for)h(creating)f(suc)n(h)h(a)g(la)n(y)n(er.)35 b(In)26 b(that)h(case,)f(the)515 3910 y(a)n(v)n(eraged)f(width)j(of)f (the)h(w)n(etting)g(la)n(y)n(er)e(is)h(of)h(order)e FA(\025)2273 3880 y Fv(\000)p Fx(1)p Fz(=)p Fx(3)2457 3910 y FB(when)i FA(d)23 b FB(=)g(1)k([22)o(].)639 4009 y(In)k(the)f(Subsection)g(1.3,)g (w)n(e)g(in)n(tro)r(duce)f(another,)h(more)f(realistic)g(mo)r (delization)h(of)515 4109 y(this)i(phenomenon)f(in)h(a)f(lattice)h (gas,)f(the)h(t)n(w)n(o-dimensional)e(Ising)h(mo)r(del,)i(and)f(pro)n (v)n(e)515 4209 y(some)37 b(partial)f(results)h(indicating)h(that)f (this)h(mo)r(del)g(has)f(the)h(same)f(t)n(yp)r(e)g(of)h(critical)515 4308 y(b)r(eha)n(vior,)26 b(in)i(particular)e(that)i(the)g(critical)f (exp)r(onen)n(t)g(is)h(also)e(1)p FA(=)p FB(3.)515 4537 y FC(1.2)112 b(Some)31 b(additional)h(results)f(ab)s(out)g(e\013ectiv)m (e)f(in)m(terface)h(mo)s(d-)770 4654 y(els)515 4807 y FB(In)21 b(this)h(section,)g(w)n(e)f(presen)n(t)g(some)f(new)i(results) e(ab)r(out)i(e\013ectiv)n(e)f(in)n(terface)g(mo)r(dels,)h(not)515 4907 y(directly)28 b(related)h(to)g(the)g(main)g(problem)f(in)n(v)n (estigated)g(in)h(the)h(pap)r(er.)40 b(Some)29 b(turn)g(out)515 5006 y(to)e(b)r(e)h(useful)g(in)g(the)g(pro)r(of)f(of)h(Theorem)e(1,)i (other)f(are)f(just)i(of)g(indep)r(enden)n(t)g(in)n(terest.)p Black Black eop end %%Page: 4 4 TeXDict begin 4 3 bop Black 515 232 a Fr(En)n(tropic)22 b(repulsion)g(in)f(external)h(\014eld;)g(v)n(ersion)f(from)g(July)g(3,) f(2003)1159 b FB(4)p Black 639 523 a(The)33 b(\014rst)f(problem)g (concerns)f(the)h(probabilit)n(y)g(that)g(an)g(in)n(terface)g(sta)n(ys) f(inside)h(a)515 623 y(\014xed)26 b(horizon)n(tal)f(slab.)36 b(This)26 b(problem)g(w)n(as)g(\014rst)g(in)n(v)n(estigated)f(in)i([9)o (])g(in)f(the)h(Gaussian)515 722 y(case.)35 b(Our)26 b(\014rst)g(result)h(in)f(an)h(extension)f(to)g(the)h(case)e(of)i (strictly)f(con)n(v)n(ex)f(in)n(teractions;)515 822 y(our)k(pro)r(of)h (is)h(also)e(completely)h(di\013eren)n(t.)46 b(Let)30 b(P)2138 834 y Fz(N)2231 822 y FB(denote)h(the)f(Gibbs)h(measure)f (with)515 922 y(0-b.c.)36 b(without)28 b(the)g(p)r(ositivit)n(y)f (constrain)n(t)g(and)g(with)h FA(\025)c FB(=)f FA(\021)j FB(=)c(0.)p Black 515 1088 a Fp(Theorem)31 b(2)p Black 41 w Fo(Ther)l(e)f(exist)f(strictly)g(p)l(ositive)h(c)l(onstants)f FA(c)2417 1100 y Fv(\000)2473 1088 y FB(\()p FA(d)p FB(\))p Fo(,)h FA(c)2671 1100 y Fx(+)2726 1088 y FB(\()p FA(d)p FB(\))p Fo(,)g FA(c)f Fo(and)g FA(`)3148 1100 y Fx(0)3208 1088 y FA(<)23 b Fy(1)515 1187 y Fo(such)30 b(that,)g(for)g(any)g FA(`)23 b(>)g(`)1371 1199 y Fx(0)1437 1187 y Fo(the)30 b(fol)t(lowing)i(holds:)p Black 639 1340 a Fy(\017)p Black 41 w Fo(If)e FA(d)24 b FB(=)e(2)p Fo(,)30 b(for)h(al)t(l)f FA(N)i(>)23 b(e)1537 1310 y Fz(c`)1598 1340 y Fo(,)1087 1521 y FA(e)1126 1486 y Fv(\000)p Fz(e)1209 1460 y Fn(\000)p Fu(c)1281 1473 y Fm(+)1328 1460 y Fu(`)1368 1486 y Fv(j)p Fx(\003)1433 1494 y Fu(N)1487 1486 y Fv(j)1534 1521 y Fy(\025)f FB(P)1678 1533 y Fz(N)1741 1521 y FB(\()p Fy(j)p FA(X)1865 1533 y Fz(i)1893 1521 y Fy(j)h(\024)f FA(`;)28 b Fy(8)p FA(i)22 b Fy(2)i FB(\003)2346 1533 y Fz(N)2408 1521 y FB(\))g Fy(\025)e FA(e)2590 1486 y Fv(\000)p Fz(e)2673 1460 y Fn(\000)p Fu(c)2745 1473 y Fn(\000)2795 1460 y Fu(`)2835 1486 y Fv(j)p Fx(\003)2900 1494 y Fu(N)2953 1486 y Fv(j)2991 1521 y FA(:)p Black 639 1728 a Fy(\017)p Black 41 w Fo(If)30 b FA(d)24 b Fy(\025)e FB(3)p Fo(,)30 b(for)h(al)t(l)f FA(N)i(>)23 b(e)1537 1698 y Fz(c`)1595 1673 y Fm(2)1631 1728 y Fo(,)1055 1923 y FA(e)1094 1889 y Fv(\000)p Fz(e)1177 1863 y Fn(\000)p Fu(c)1249 1876 y Fm(+)1296 1863 y Fu(`)1321 1846 y Fm(2)1368 1889 y Fv(j)p Fx(\003)1433 1897 y Fu(N)1487 1889 y Fv(j)1534 1923 y Fy(\025)f FB(P)1678 1935 y Fz(N)1741 1923 y FB(\()p Fy(j)p FA(X)1865 1935 y Fz(i)1893 1923 y Fy(j)h(\024)f FA(`;)28 b Fy(8)p FA(i)22 b Fy(2)i FB(\003)2346 1935 y Fz(N)2408 1923 y FB(\))g Fy(\025)e FA(e)2590 1889 y Fv(\000)p Fz(e)2673 1863 y Fn(\000)p Fu(c)2745 1876 y Fn(\000)2795 1863 y Fu(`)2820 1846 y Fm(2)2867 1889 y Fv(j)p Fx(\003)2932 1897 y Fu(N)2986 1889 y Fv(j)3023 1923 y FA(:)515 2119 y FB(W)-7 b(e)21 b(ha)n(v)n(e)f(not)g(b)r(een)i (able)e(to)h(extend)g(the)g(results)f(on)h(the)g(v)-5 b(ariance)20 b(and)g(the)i(mass)e(pro)n(v)n(ed)515 2219 y(in)30 b([9)o(])g(in)g(the)g(Gaussian)e(setting.)43 b(The)29 b(corresp)r(onding)f(results)h(in)h(dimension)f(1,)h(v)-5 b(alid)515 2319 y(for)27 b(a)g(m)n(uc)n(h)g(larger)f(class)h(of)g(mo)r (dels)h(will)g(app)r(ear)e(in)i([22)o(])639 2461 y(All)i(other)f (results)g(concern)f(the)i(\(pure\))g(w)n(etting)f(transition)g(in)g (e\013ectiv)n(e)h(in)n(terface)515 2561 y(mo)r(dels.)36 b(W)-7 b(e)25 b(start)f(with)i(results)e(giving)g(more)g(informations)g (on)h(path)n(wise)f(prop)r(erties.)p Black 515 2714 a Fp(Theorem)31 b(3)p Black Black 139 w Fo(1.)p Black 43 w(L)l(et)c FA(\035)f Fy(2)d Ft(CW)r Fo(.)37 b(F)-6 b(or)28 b(al)t(l)g FA(\017)23 b(>)g FB(0)p Fo(,)k(ther)l(e)h(exist)f FA(N)2673 2726 y Fx(0)2710 2714 y FB(\()p FA(\035)s(;)14 b(\017)p FB(\))27 b Fo(and)g FA(c)p FB(\()p FA(\035)s FB(\))d FA(>)e FB(0)722 2814 y Fo(such)30 b(that,)g(for)h(al)t(l)g FA(N)h Fy(\025)22 b FA(N)1611 2826 y Fx(0)1648 2814 y Fo(,)1195 2992 y FB(P)1252 3004 y Fz(N)s(;)p Fx(+)p Fz(;)p Fx(0)p Fz(;\035)1493 2992 y FB(\()p Fy(j)p FB(\003)1606 3004 y Fz(N)1669 2992 y Fy(j)1692 2957 y Fv(\000)p Fx(1)1833 2913 y Fw(X)1809 3091 y Fz(i)p Fv(2)p Fx(\003)1922 3099 y Fu(N)1990 2992 y FB(1)2032 3007 y Fv(f)p Fz(X)2120 3015 y Fu(i)2146 3007 y Fx(=0)p Fv(g)2292 2992 y Fy(\025)g FA(\017)p FB(\))h Fy(\024)g FA(e)2595 2957 y Fv(\000)p Fz(c)11 b(\017)g Fv(j)p Fx(\003)2792 2965 y Fu(N)2845 2957 y Fv(j)2883 2992 y FA(:)p Black 613 3270 a Fo(2.)p Black 42 w(L)l(et)30 b FA(d)23 b FB(=)g(2)29 b Fo(and)h FA(\035)c Fy(2)d Ft(CW)r Fo(.)1409 3436 y FB(lim)1371 3489 y Fz(N)6 b Fv(!1)1576 3436 y FB(E)1633 3448 y Fz(N)s(;)p Fx(+)p Fz(;)p Fx(0)p Fz(;\035)1874 3436 y FB(\()p Fy(j)p FB(\003)1987 3448 y Fz(N)2050 3436 y Fy(j)2073 3402 y Fv(\000)p Fx(1)2214 3357 y Fw(X)2190 3535 y Fz(i)p Fv(2)p Fx(\003)2303 3543 y Fu(N)2371 3436 y FA(X)2440 3448 y Fz(i)2467 3436 y FB(\))24 b(=)e Fy(1)14 b FA(:)722 3684 y Fo(Mor)l(e)l(over,)32 b(for)e(al)t(l)h FA(\021)i Fo(smal)t(l)e (enough,)f(ther)l(e)g(exists)g FA(C)f(>)23 b FB(0)29 b Fo(such)h(that)1377 3862 y FB(E)1434 3874 y Fz(N)s(;)p Fx(+)p Fz(;)p Fx(0)p Fz(;\035)1675 3862 y FB(\()p Fy(j)p FB(\003)1788 3874 y Fz(N)1851 3862 y Fy(j)1874 3828 y Fv(\000)p Fx(1)2015 3783 y Fw(X)1991 3962 y Fz(i)p Fv(2)p Fx(\003)2104 3970 y Fu(N)2172 3862 y FA(X)2241 3874 y Fz(i)2268 3862 y FB(\))24 b Fy(\025)e FA(C)e FB(log)14 b FA(N)23 b(:)p Black 613 4150 a Fo(3.)p Black 42 w(We)35 b(c)l(onsider)i(the)e(Gaussian)g(c)l(ase)h Ft(U)p FB(\()p FA(x)p FB(\))e(=)e FA(x)2253 4120 y Fx(2)2291 4150 y FA(=)p FB(2)p Fo(.)53 b(L)l(et)35 b FA(d)e FB(=)f(2)j Fo(and)g FA(\035)j Fo(b)l(e)d(lar)l(ge)722 4250 y(enough.)k(Then)31 b(ther)l(e)f(exists)f FA(C)g(<)23 b Fy(1)30 b Fo(such)g(that,)g(for)g (al)t(l)h FA(i)23 b Fy(2)g FB(\003)2801 4262 y Fz(N)2864 4250 y Fo(,)1715 4416 y FB(E)1772 4428 y Fz(N)s(;)p Fx(+)p Fz(;)p Fx(0)p Fz(;\035)2013 4416 y FB(\()p FA(X)2114 4428 y Fz(i)2141 4416 y FB(\))h Fy(\024)e FA(C)f(:)722 4582 y Fo(Mor)l(e)l(over,)32 b(ther)l(e)e(exists)f FA(C)g(>)23 b FB(0)29 b Fo(such)h(that,)g(for)h(al)t(l)g FA(x)23 b Fy(2)h Fq(S)2625 4552 y Fx(1)2662 4582 y Fo(,)1236 4783 y FB(lim)1209 4837 y Fz(k)q Fv(!1)1392 4783 y Fy(\000)1469 4727 y FB(1)p 1467 4764 46 4 v 1467 4840 a FA(k)1536 4783 y FB(lim)14 b(sup)1567 4853 y Fz(N)6 b Fv(!1)1804 4783 y FB(log)14 b(co)n(v)2046 4795 y Fz(N)s(;)p Fx(+)p Fz(;)p Fx(0)p Fz(;\035)2287 4783 y FB(\()p FA(X)2388 4795 y Fx(0)2426 4783 y FA(;)g(X)2532 4798 y Fx([)p Fz(k)q(x)p Fx(])2647 4783 y FB(\))24 b FA(>)e(C)f(;)722 5006 y Fo(wher)l(e)31 b FB([)p FA(y)s FB(])23 b Fy(2)g Fq(Z)1203 4976 y Fz(d)1272 5006 y Fo(denotes)30 b(the)g(c)l(omp)l(onentwise)g(inte)l(ger)g(p)l (art)g(of)h FA(y)25 b Fy(2)f Fq(R)3026 4976 y Fz(d)3064 5006 y Fo(.)p Black Black eop end %%Page: 5 5 TeXDict begin 5 4 bop Black 515 232 a Fr(En)n(tropic)22 b(repulsion)g(in)f(external)h(\014eld;)g(v)n(ersion)f(from)g(July)g(3,) f(2003)1159 b FB(5)p Black 515 523 a(Finally)-7 b(,)34 b(a)e(long-term)g(goal)f(w)n(ould)i(b)r(e)g(to)f(con)n(trol)g(quan)n (titativ)n(ely)g(the)h(div)n(ergence)e(of)515 623 y(the)i(in)n(terface) g(as)g(the)g(w)n(etting)g(transition)g(is)g(approac)n(hed)e(from)i(the) h(partial)e(w)n(etting)515 722 y(regime,)e(i.e.)45 b(the)31 b(limit)g FA(\035)f Fy(&)e FA(\035)1538 734 y Fx(c)1571 722 y FB(.)46 b(This)30 b(seems)g(far)g(from)g(what)g(can)g(b)r(e)g(ac) n(hiev)n(ed)g(with)515 822 y(to)r(da)n(y's)19 b(tec)n(hniques,)j(but)f (at)g(least)f(w)n(e)g(can)g(sho)n(w)g(\(easily\),)i(in)e(the)h FA(d)j Fy(\025)e FB(3)e(Gaussian)g(case,)515 922 y(that)34 b(the)h(transition)e(is)h(second)g(order,)g(in)g(the)h(sense)e(that)i (the)f(a)n(v)n(erage)e(heigh)n(t)h(do)r(es)515 1021 y(indeed)28 b(div)n(erge)e(as)h FA(\035)f Fy(&)d FA(\035)1388 1033 y Fx(c)1444 1021 y FB(=)g(0,)k(and)h(not)f(sta)n(y)g(\014nite)h(and)g (jump)g(at)g(the)f(transition.)p Black 515 1185 a Fp(Theorem)k(4)p Black 41 w Fo(L)l(et)36 b FA(d)f Fy(\025)f FB(3)h Fo(and)i(supp)l(ose)f (that)g FA(\035)2111 1197 y Fx(c)2179 1185 y FB(=)e(0)i Fo(\(this)g(is)h(the)f(c)l(ase,)i(e.g.,)i(when)515 1285 y Ft(U)p FB(\()p FA(x)p FB(\))24 b(=)f FA(x)842 1255 y Fx(2)879 1285 y FA(=)p FB(2)p Fo(\).)38 b(Then,)31 b(for)f(any)g FA(i)23 b Fy(2)h Fq(Z)1779 1255 y Fz(d)1818 1285 y Fo(,)1432 1466 y FB(lim)1404 1520 y Fz(\035)r Fv(&)p Fz(\035)1546 1528 y Fm(c)1627 1466 y FB(lim)1589 1519 y Fz(N)6 b Fv(!1)1794 1466 y FB(E)1851 1478 y Fz(N)s(;)p Fx(+)p Fz(;\025;\035)2098 1466 y FB(\()p FA(X)2199 1478 y Fz(i)2227 1466 y FB(\))23 b(=)g Fy(1)14 b FA(:)515 1733 y FC(1.3)112 b(The)38 b(t)m(w)m(o-dimensional)h(Ising)f(mo)s(del) 515 1886 y FB(It)28 b(w)n(ould)f(of)g(course)f(b)r(e)i(v)n(ery)e(in)n (teresting)h(to)h(obtain)f(results)g(similar)f(to)i(those)f(of)g(The-) 515 1986 y(orem)j(1)h(also)f(in)h(the)h(case)e(of)h(lattice)g(gases.)46 b(Ho)n(w)n(ev)n(er,)31 b(suc)n(h)f(systems)h(do)g(not)g(alw)n(a)n(ys) 515 2085 y(displa)n(y)j(critical)g(prew)n(etting.)58 b(In)35 b(particular,)g(b)r(elo)n(w)g(the)g(roughening)e(temp)r (erature,)515 2185 y(e.g.)52 b(in)34 b(the)f(lo)n(w-temp)r(erature)f (3-dimensional)f(Ising)i(mo)r(del,)h(or)f(in)g(sub)r(critical)g(Ising) 515 2284 y(mo)r(dels)23 b(in)h(dimensions)f FA(d)g Fy(\025)f FB(4,)i(it)g(is)f(exp)r(ected)h(that)g(the)f(con)n(tin)n(uous)g(div)n (ergence)e(of)j(the)515 2384 y(width)c(of)f(the)g(w)n(et)h(la)n(y)n(er) d(is)i(replaced)g(b)n(y)f(an)h(in\014nite)h(sequence)f(of)g(\014rst)g (order)f(phase)h(tran-)515 2484 y(sitions,)j(the)f Fo(layering)k(tr)l (ansitions)p FB(,)d(at)f(whic)n(h)g(the)g(in)n(terface)f(jumps)i(up)f (one)g(microscopic)515 2583 y(unit.)45 b(This)31 b(has)e(nev)n(er)h(b)r (een)g(established)g(for)g(the)h(Ising)f(mo)r(del,)h(though)f(that)g (should)515 2683 y(follo)n(w)38 b(from)h(a)h(rather)e(straigh)n(tforw)n (ard,)h(but)h(tec)n(hnically)f(in)n(v)n(olv)n(ed,)i(Pirogo)n(v-Sinai) 515 2783 y(analysis.)c(This)28 b(problem)g(w)n(as)f(studied)i(in)f (detail)g(in)h(the)f(series)g(of)g(pap)r(ers)f([18)o(,)i(13)o(,)f(25)o (])515 2882 y(in)g(the)g(case)e(of)i(the)g(discrete)f(SOS)g(mo)r(del.) 639 2982 y(On)19 b(the)g(other)f(hand,)j(critical)d(prew)n(etting)g(is) h(exp)r(ected)g(to)g(o)r(ccur)f(in)h(the)g(rough)f(phase)515 3081 y(of)29 b(suc)n(h)g(mo)r(dels.)42 b(In)30 b(particular,)e(it)i (should)f(o)r(ccur)g(for)g(an)n(y)g(sub)r(critical)g(temp)r(eratures) 515 3181 y(in)e(the)f(case)g(of)h(the)f(t)n(w)n(o-dimensional)f(Ising)h (mo)r(del.)37 b(This)27 b(is)f(what)g(w)n(e)h(analyze)e(in)i(this)515 3281 y(section.)639 3478 y(Let)22 b FA(N)31 b FB(b)r(e)22 b(ev)n(en)g(and)f(set)h(\003)1508 3490 y Fz(N)1594 3478 y FB(=)h Fy(f\000)p FA(N)r(=)p FB(2)7 b(+)g(1)p FA(;)14 b(:)g(:)g(:)c(;)k(N)r(=)p FB(2)p Fy(g)7 b(\002)g(f)p FB(0)p FA(;)14 b(:)g(:)g(:)d(;)j(N)h Fy(\000)7 b FB(1)p Fy(g)p FB(,)22 b FA(@)3116 3448 y Fx(+)3171 3478 y FB(\003)3229 3490 y Fz(N)3314 3478 y FB(=)515 3578 y Fy(f)p FA(x)37 b Fy(2)i FB(\003)793 3590 y Fz(N)907 3578 y FB(:)51 b Fy(9)p FA(y)41 b Fy(62)d FB(\003)1260 3590 y Fz(N)1323 3578 y FA(;)27 b Fy(j)p FA(x)e Fy(\000)f FA(y)s Fy(j)38 b FB(=)f(1)p FA(;)27 b(y)1897 3590 y Fx(2)1972 3578 y Fy(\025)37 b FB(0)p Fy(g)f FB(and)g FA(@)2413 3548 y Fv(\000)2469 3578 y FB(\003)2527 3590 y Fz(N)2627 3578 y FB(=)h Fy(f)p FA(x)h Fy(2)g FB(\003)3007 3590 y Fz(N)3121 3578 y FB(:)52 b Fy(9)p FA(y)41 b Fy(62)515 3677 y FB(\003)573 3689 y Fz(N)635 3677 y FA(;)28 b Fy(j)p FA(x)19 b Fy(\000)f FA(y)s Fy(j)23 b FB(=)g(1)p FA(;)k(y)1169 3689 y Fx(2)1229 3677 y FB(=)22 b Fy(\000)p FB(1)p Fy(g)p FB(.)639 3777 y(W)-7 b(e)21 b(de\014ne)f(the)h(follo)n(wing)e(Hamiltonian)h(acting)f (on)h(con\014gurations)f FA(\033)26 b Fy(2)e(f\000)p FB(1)p FA(;)14 b FB(1)p Fy(g)3256 3747 y Fx(\003)3301 3755 y Fu(N)3356 3777 y FB(,)660 3974 y FA(H)729 3986 y Fz(\025;h;)p Fx(\003)892 3994 y Fu(N)950 3974 y FB(\()p FA(\033)s FB(\))24 b(=)e Fy(\000)1343 3895 y Fw(X)1254 4077 y Fv(h)p Fz(x;y)r Fv(i\032)p Fx(\003)1499 4085 y Fu(N)1565 3974 y FA(\033)1612 3986 y Fz(x)1654 3974 y FA(\033)1701 3986 y Fz(y)1760 3974 y Fy(\000)c FA(\025)1936 3895 y Fw(X)1905 4073 y Fz(x)p Fv(2)p Fx(\003)2033 4081 y Fu(N)2100 3974 y FA(\033)2147 3986 y Fz(x)2208 3974 y Fy(\000)2365 3895 y Fw(X)2291 4078 y Fz(x)p Fv(2)p Fz(@)2413 4061 y Fm(+)2459 4078 y Fx(\003)2504 4086 y Fu(N)2572 3974 y FA(\033)2619 3986 y Fz(x)2680 3974 y FB(+)g FA(h)2899 3895 y Fw(X)2825 4078 y Fz(x)p Fv(2)p Fz(@)2947 4061 y Fn(\000)2995 4078 y Fx(\003)3040 4086 y Fu(N)3108 3974 y FA(\033)3155 3986 y Fz(x)3211 3974 y FA(:)515 4247 y(\025)23 b(>)g FB(0)h(is)h(the)g(bulk)f(magnetic)h (\014eld,)g(while)g(the)g(b)r(oundary)f(\014eld)h FA(h)e(>)f FB(0)i(serv)n(es)f(to)i(mo)r(del)515 4346 y(the)h(preference)f(of)h (the)g(b)r(ottom)g(w)n(all)g(to)n(w)n(ard)e Fy(\000)h FB(spins.)37 b(The)25 b(Gibbs)i(measure)d(in)j(\003)3235 4358 y Fz(N)3323 4346 y FB(is)515 4446 y(the)h(probabilit)n(y)e (measure)h(on)g FA(\033)g Fy(2)c(f\000)p FB(1)p FA(;)14 b FB(1)p Fy(g)1943 4416 y Fx(\003)1988 4424 y Fu(N)2071 4446 y FB(giv)n(en)27 b(b)n(y)1145 4627 y FA(\026)1195 4639 y Fz(\014)s(;\025;h;)p Fx(\003)1419 4647 y Fu(N)1476 4627 y FB(\()p FA(\033)s FB(\))d(=)f(\()p FA(Z)1791 4639 y Fz(\014)s(;\025;h;)p Fx(\003)2015 4647 y Fu(N)2071 4627 y FB(\))2103 4592 y Fv(\000)p Fx(1)2216 4627 y FA(e)2255 4592 y Fv(\000)p Fz(\014)13 b(H)2412 4601 y Fu(\025;h;)p Fm(\003)2557 4615 y Fu(N)2615 4592 y Fx(\()p Fz(\033)r Fx(\))2726 4627 y FA(:)639 4807 y FB(Let)32 b FA(\014)j(>)30 b(\014)1016 4819 y Fz(c)1082 4807 y FB(and)i FA(\025)f FB(=)f(0.)49 b(Because)31 b(of)h(our)g(c)n(hoice)f(of)h(b)r(oundary)f (conditions,)i(the)515 4907 y(bulk)38 b(of)f(the)i(system)e(is)h(o)r (ccupied,)i(with)e(probabilit)n(y)f(asymptotically)g(1,)j(b)n(y)d(the)h (+)515 5006 y(phase,)29 b(while)g(the)g(in)n(tro)r(duction)g(of)g(the)g (b)r(oundary)g(\014eld)g FA(h)g FB(results)f(in)i(the)f(creation)f(of)p Black Black eop end %%Page: 6 6 TeXDict begin 6 5 bop Black 515 232 a Fr(En)n(tropic)22 b(repulsion)g(in)f(external)h(\014eld;)g(v)n(ersion)f(from)g(July)g(3,) f(2003)1159 b FB(6)p Black Black 1386 1503 a @beginspecial 0 @llx 0 @lly 364 @urx 345 @ury 1275 @rhi @setspecial %%BeginDocument: layervol.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: layervol.eps %%Creator: fig2dev Version 3.2 Patchlevel 3d %%CreationDate: Wed Nov 28 14:31:41 2001 %%For: velenik@latpcmi22.cmi.univ-mrs.fr (Yvan VELENIK, CR probabilites) %%BoundingBox: 0 0 364 345 %%Magnification: 1.0000 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save newpath 0 345 moveto 0 0 lineto 364 0 lineto 364 345 lineto closepath clip newpath -142.0 425.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def $F2psBegin 10 setmiterlimit 0.06000 0.06000 sc % % Fig objects follow % % Polyline n 2850 7050 m 2850 6750 l 3450 6750 l 3450 6450 l 3150 6450 l 3150 6150 l 3450 6150 l 3450 6450 l 3750 6450 l 3750 6150 l 5250 6150 l 5250 6450 l 5850 6450 l 5850 6150 l 5250 6150 l 5250 5550 l 5850 5550 l 5850 5850 l 6450 5850 l 6450 6150 l 6450 6150 l 7350 6150 l 7350 6450 l 7950 6450 l 7950 6750 l 8250 6750 l 8250 7050 l cp gs col7 0.85 shd ef gr % Polyline 7.500 slw n 2625 6900 m 2775 6900 l gs col0 s gr % Polyline n 2700 6825 m 2700 6975 l gs col0 s gr % Polyline n 3825 6900 m 3975 6900 l gs col0 s gr % Polyline n 3900 6825 m 3900 6975 l gs col0 s gr % Polyline n 5325 6900 m 5475 6900 l gs col0 s gr % Polyline n 5400 6825 m 5400 6975 l gs col0 s gr % Polyline n 6225 6900 m 6375 6900 l gs col0 s gr % Polyline n 6300 6825 m 6300 6975 l gs col0 s gr % Polyline n 7425 6900 m 7575 6900 l gs col0 s gr % Polyline n 7500 6825 m 7500 6975 l gs col0 s gr % Polyline n 2625 6600 m 2775 6600 l gs col0 s gr % Polyline n 2700 6525 m 2700 6675 l gs col0 s gr % Polyline n 2925 6600 m 3075 6600 l gs col0 s gr % Polyline n 3000 6525 m 3000 6675 l gs col0 s gr % Polyline n 3225 6600 m 3375 6600 l gs col0 s gr % Polyline n 3300 6525 m 3300 6675 l gs col0 s gr % Polyline n 4125 6600 m 4275 6600 l gs col0 s gr % Polyline n 4200 6525 m 4200 6675 l gs col0 s gr % Polyline n 4725 6600 m 4875 6600 l gs col0 s gr % Polyline n 4800 6525 m 4800 6675 l gs col0 s gr % Polyline n 6825 6600 m 6975 6600 l gs col0 s gr % Polyline n 6900 6525 m 6900 6675 l gs col0 s gr % Polyline n 8025 6600 m 8175 6600 l gs col0 s gr % Polyline n 8100 6525 m 8100 6675 l gs col0 s gr % Polyline n 2625 6300 m 2775 6300 l gs col0 s gr % Polyline n 2700 6225 m 2700 6375 l gs col0 s gr % Polyline n 2925 6300 m 3075 6300 l gs col0 s gr % Polyline n 3000 6225 m 3000 6375 l gs col0 s gr % Polyline n 3525 6300 m 3675 6300 l gs col0 s gr % Polyline n 3600 6225 m 3600 6375 l gs col0 s gr % Polyline n 5325 6300 m 5475 6300 l gs col0 s gr % Polyline n 5400 6225 m 5400 6375 l gs col0 s gr % Polyline n 5625 6300 m 5775 6300 l gs col0 s gr % Polyline n 5700 6225 m 5700 6375 l gs col0 s gr % Polyline n 6225 6300 m 6375 6300 l gs col0 s gr % Polyline n 6300 6225 m 6300 6375 l gs col0 s gr % Polyline n 7425 6300 m 7575 6300 l gs col0 s gr % Polyline n 7500 6225 m 7500 6375 l gs col0 s gr % Polyline n 7725 6300 m 7875 6300 l gs col0 s gr % Polyline n 7800 6225 m 7800 6375 l gs col0 s gr % Polyline n 8025 6300 m 8175 6300 l gs col0 s gr % Polyline n 8100 6225 m 8100 6375 l gs col0 s gr % Polyline n 2625 6000 m 2775 6000 l gs col0 s gr % Polyline n 2700 5925 m 2700 6075 l gs col0 s gr % Polyline n 2925 6000 m 3075 6000 l gs col0 s gr % Polyline n 3000 5925 m 3000 6075 l gs col0 s gr % Polyline n 3225 6000 m 3375 6000 l gs col0 s gr % Polyline n 3300 5925 m 3300 6075 l gs col0 s gr % Polyline n 3525 6000 m 3675 6000 l gs col0 s gr % Polyline n 3600 5925 m 3600 6075 l gs col0 s gr % Polyline n 3825 6000 m 3975 6000 l gs col0 s gr % Polyline n 3900 5925 m 3900 6075 l gs col0 s gr % Polyline n 4125 6000 m 4275 6000 l gs col0 s gr % Polyline n 4200 5925 m 4200 6075 l gs col0 s gr % Polyline n 4425 6000 m 4575 6000 l gs col0 s gr % Polyline n 4500 5925 m 4500 6075 l gs col0 s gr % Polyline n 4725 6000 m 4875 6000 l gs col0 s gr % Polyline n 4800 5925 m 4800 6075 l gs col0 s gr % Polyline n 5025 6000 m 5175 6000 l gs col0 s gr % Polyline n 5100 5925 m 5100 6075 l gs col0 s gr % Polyline n 6525 6000 m 6675 6000 l gs col0 s gr % Polyline n 6600 5925 m 6600 6075 l gs col0 s gr % Polyline n 6825 6000 m 6975 6000 l gs col0 s gr % Polyline n 6900 5925 m 6900 6075 l gs col0 s gr % Polyline n 7125 6000 m 7275 6000 l gs col0 s gr % Polyline n 7200 5925 m 7200 6075 l gs col0 s gr % Polyline n 7725 6000 m 7875 6000 l gs col0 s gr % Polyline n 7800 5925 m 7800 6075 l gs col0 s gr % Polyline n 8025 6000 m 8175 6000 l gs col0 s gr % Polyline n 8100 5925 m 8100 6075 l gs col0 s gr % Polyline n 2625 5700 m 2775 5700 l gs col0 s gr % Polyline n 2700 5625 m 2700 5775 l gs col0 s gr % Polyline n 2925 5700 m 3075 5700 l gs col0 s gr % Polyline n 3000 5625 m 3000 5775 l gs col0 s gr % Polyline n 3225 5700 m 3375 5700 l gs col0 s gr % Polyline n 3300 5625 m 3300 5775 l gs col0 s gr % Polyline n 3525 5700 m 3675 5700 l gs col0 s gr % Polyline n 3600 5625 m 3600 5775 l gs col0 s gr % Polyline n 4125 5700 m 4275 5700 l gs col0 s gr % Polyline n 4200 5625 m 4200 5775 l gs col0 s gr % Polyline n 4425 5700 m 4575 5700 l gs col0 s gr % Polyline n 4500 5625 m 4500 5775 l gs col0 s gr % Polyline n 4725 5700 m 4875 5700 l gs col0 s gr % Polyline n 4800 5625 m 4800 5775 l gs col0 s gr % Polyline n 5025 5700 m 5175 5700 l gs col0 s gr % Polyline n 5100 5625 m 5100 5775 l gs col0 s gr % Polyline n 5925 5700 m 6075 5700 l gs col0 s gr % Polyline n 6000 5625 m 6000 5775 l gs col0 s gr % Polyline n 6225 5700 m 6375 5700 l gs col0 s gr % Polyline n 6300 5625 m 6300 5775 l gs col0 s gr % Polyline n 6525 5700 m 6675 5700 l gs col0 s gr % Polyline n 6600 5625 m 6600 5775 l gs col0 s gr % Polyline n 6825 5700 m 6975 5700 l gs col0 s gr % Polyline n 6900 5625 m 6900 5775 l gs col0 s gr % Polyline n 7125 5700 m 7275 5700 l gs col0 s gr % Polyline n 7200 5625 m 7200 5775 l gs col0 s gr % Polyline n 7425 5700 m 7575 5700 l gs col0 s gr % Polyline n 7500 5625 m 7500 5775 l gs col0 s gr % Polyline n 7725 5700 m 7875 5700 l gs col0 s gr % Polyline n 7800 5625 m 7800 5775 l gs col0 s gr % Polyline n 8025 5700 m 8175 5700 l gs col0 s gr % Polyline n 8100 5625 m 8100 5775 l gs col0 s gr % Polyline n 2625 5400 m 2775 5400 l gs col0 s gr % Polyline n 2700 5325 m 2700 5475 l gs col0 s gr % Polyline n 2925 5400 m 3075 5400 l gs col0 s gr % Polyline n 3000 5325 m 3000 5475 l gs col0 s gr % Polyline n 3225 5400 m 3375 5400 l gs col0 s gr % Polyline n 3300 5325 m 3300 5475 l gs col0 s gr % Polyline n 3525 5400 m 3675 5400 l gs col0 s gr % Polyline n 3600 5325 m 3600 5475 l gs col0 s gr % Polyline n 3825 5400 m 3975 5400 l gs col0 s gr % Polyline n 3900 5325 m 3900 5475 l gs col0 s gr % Polyline n 4125 5400 m 4275 5400 l gs col0 s gr % Polyline n 4200 5325 m 4200 5475 l gs col0 s gr % Polyline n 4425 5400 m 4575 5400 l gs col0 s gr % Polyline n 4500 5325 m 4500 5475 l gs col0 s gr % Polyline n 4725 5400 m 4875 5400 l gs col0 s gr % Polyline n 4800 5325 m 4800 5475 l gs col0 s gr % Polyline n 5025 5400 m 5175 5400 l gs col0 s gr % Polyline n 5100 5325 m 5100 5475 l gs col0 s gr % Polyline n 5325 5400 m 5475 5400 l gs col0 s gr % Polyline n 5400 5325 m 5400 5475 l gs col0 s gr % Polyline n 5625 5400 m 5775 5400 l gs col0 s gr % Polyline n 5700 5325 m 5700 5475 l gs col0 s gr % Polyline n 5925 5400 m 6075 5400 l gs col0 s gr % Polyline n 6000 5325 m 6000 5475 l gs col0 s gr % Polyline n 6225 5400 m 6375 5400 l gs col0 s gr % Polyline n 6300 5325 m 6300 5475 l gs col0 s gr % Polyline n 6525 5400 m 6675 5400 l gs col0 s gr % Polyline n 6600 5325 m 6600 5475 l gs col0 s gr % Polyline n 6825 5400 m 6975 5400 l gs col0 s gr % Polyline n 6900 5325 m 6900 5475 l gs col0 s gr % Polyline n 7125 5400 m 7275 5400 l gs col0 s gr % Polyline n 7200 5325 m 7200 5475 l gs col0 s gr % Polyline n 7725 5400 m 7875 5400 l gs col0 s gr % Polyline n 7800 5325 m 7800 5475 l gs col0 s gr % Polyline n 8025 5400 m 8175 5400 l gs col0 s gr % Polyline n 8100 5325 m 8100 5475 l gs col0 s gr % Polyline n 2625 5100 m 2775 5100 l gs col0 s gr % Polyline n 2700 5025 m 2700 5175 l gs col0 s gr % Polyline n 2925 5100 m 3075 5100 l gs col0 s gr % Polyline n 3000 5025 m 3000 5175 l gs col0 s gr % Polyline n 3225 5100 m 3375 5100 l gs col0 s gr % Polyline n 3300 5025 m 3300 5175 l gs col0 s gr % Polyline n 3525 5100 m 3675 5100 l gs col0 s gr % Polyline n 3600 5025 m 3600 5175 l gs col0 s gr % Polyline n 3825 5100 m 3975 5100 l gs col0 s gr % Polyline n 3900 5025 m 3900 5175 l gs col0 s gr % Polyline n 4125 5100 m 4275 5100 l gs col0 s gr % Polyline n 4200 5025 m 4200 5175 l gs col0 s gr % Polyline n 4425 5100 m 4575 5100 l gs col0 s gr % Polyline n 4500 5025 m 4500 5175 l gs col0 s gr % Polyline n 5025 5100 m 5175 5100 l gs col0 s gr % Polyline n 5100 5025 m 5100 5175 l gs col0 s gr % Polyline n 5325 5100 m 5475 5100 l gs col0 s gr % Polyline n 5400 5025 m 5400 5175 l gs col0 s gr % Polyline n 5625 5100 m 5775 5100 l gs col0 s gr % Polyline n 5700 5025 m 5700 5175 l gs col0 s gr % Polyline n 5925 5100 m 6075 5100 l gs col0 s gr % Polyline n 6000 5025 m 6000 5175 l gs col0 s gr % Polyline n 6225 5100 m 6375 5100 l gs col0 s gr % Polyline n 6300 5025 m 6300 5175 l gs col0 s gr % Polyline n 6525 5100 m 6675 5100 l gs col0 s gr % Polyline n 6600 5025 m 6600 5175 l gs col0 s gr % Polyline n 7125 5100 m 7275 5100 l gs col0 s gr % Polyline n 7200 5025 m 7200 5175 l gs col0 s gr % Polyline n 7425 5100 m 7575 5100 l gs col0 s gr % Polyline n 7500 5025 m 7500 5175 l gs col0 s gr % Polyline n 7725 5100 m 7875 5100 l gs col0 s gr % Polyline n 7800 5025 m 7800 5175 l gs col0 s gr % Polyline n 8025 5100 m 8175 5100 l gs col0 s gr % Polyline n 8100 5025 m 8100 5175 l gs col0 s gr % Polyline n 2625 4800 m 2775 4800 l gs col0 s gr % Polyline n 2700 4725 m 2700 4875 l gs col0 s gr % Polyline n 2925 4800 m 3075 4800 l gs col0 s gr % Polyline n 3000 4725 m 3000 4875 l gs col0 s gr % Polyline n 3525 4800 m 3675 4800 l gs col0 s gr % Polyline n 3600 4725 m 3600 4875 l gs col0 s gr % Polyline n 3825 4800 m 3975 4800 l gs col0 s gr % Polyline n 3900 4725 m 3900 4875 l gs col0 s gr % Polyline n 4125 4800 m 4275 4800 l gs col0 s gr % Polyline n 4200 4725 m 4200 4875 l gs col0 s gr % Polyline n 4425 4800 m 4575 4800 l gs col0 s gr % Polyline n 4500 4725 m 4500 4875 l gs col0 s gr % Polyline n 4725 4800 m 4875 4800 l gs col0 s gr % Polyline n 4800 4725 m 4800 4875 l gs col0 s gr % Polyline n 5025 4800 m 5175 4800 l gs col0 s gr % Polyline n 5100 4725 m 5100 4875 l gs col0 s gr % Polyline n 5325 4800 m 5475 4800 l gs col0 s gr % Polyline n 5400 4725 m 5400 4875 l gs col0 s gr % Polyline n 5625 4800 m 5775 4800 l gs col0 s gr % Polyline n 5700 4725 m 5700 4875 l gs col0 s gr % Polyline n 5925 4800 m 6075 4800 l gs col0 s gr % Polyline n 6000 4725 m 6000 4875 l gs col0 s gr % Polyline n 6225 4800 m 6375 4800 l gs col0 s gr % Polyline n 6300 4725 m 6300 4875 l gs col0 s gr % Polyline n 6525 4800 m 6675 4800 l gs col0 s gr % Polyline n 6600 4725 m 6600 4875 l gs col0 s gr % Polyline n 6825 4800 m 6975 4800 l gs col0 s gr % Polyline n 6900 4725 m 6900 4875 l gs col0 s gr % Polyline n 7125 4800 m 7275 4800 l gs col0 s gr % Polyline n 7200 4725 m 7200 4875 l gs col0 s gr % Polyline n 7425 4800 m 7575 4800 l gs col0 s gr % Polyline n 7500 4725 m 7500 4875 l gs col0 s gr % Polyline n 7725 4800 m 7875 4800 l gs col0 s gr % Polyline n 7800 4725 m 7800 4875 l gs col0 s gr % Polyline n 8025 4800 m 8175 4800 l gs col0 s gr % Polyline n 8100 4725 m 8100 4875 l gs col0 s gr % Polyline n 2625 4500 m 2775 4500 l gs col0 s gr % Polyline n 2700 4425 m 2700 4575 l gs col0 s gr % Polyline n 2925 4500 m 3075 4500 l gs col0 s gr % Polyline n 3000 4425 m 3000 4575 l gs col0 s gr % Polyline n 3225 4500 m 3375 4500 l gs col0 s gr % Polyline n 3300 4425 m 3300 4575 l gs col0 s gr % Polyline n 3525 4500 m 3675 4500 l gs col0 s gr % Polyline n 3600 4425 m 3600 4575 l gs col0 s gr % Polyline n 3825 4500 m 3975 4500 l gs col0 s gr % Polyline n 3900 4425 m 3900 4575 l gs col0 s gr % Polyline n 4125 4500 m 4275 4500 l gs col0 s gr % Polyline n 4200 4425 m 4200 4575 l gs col0 s gr % Polyline n 4425 4500 m 4575 4500 l gs col0 s gr % Polyline n 4500 4425 m 4500 4575 l gs col0 s gr % Polyline n 4725 4500 m 4875 4500 l gs col0 s gr % Polyline n 4800 4425 m 4800 4575 l gs col0 s gr % Polyline n 5025 4500 m 5175 4500 l gs col0 s gr % Polyline n 5100 4425 m 5100 4575 l gs col0 s gr % Polyline n 5325 4500 m 5475 4500 l gs col0 s gr % Polyline n 5400 4425 m 5400 4575 l gs col0 s gr % Polyline n 6225 4500 m 6375 4500 l gs col0 s gr % Polyline n 6300 4425 m 6300 4575 l gs col0 s gr % Polyline n 6525 4500 m 6675 4500 l gs col0 s gr % Polyline n 6600 4425 m 6600 4575 l gs col0 s gr % Polyline n 6825 4500 m 6975 4500 l gs col0 s gr % Polyline n 6900 4425 m 6900 4575 l gs col0 s gr % Polyline n 7125 4500 m 7275 4500 l gs col0 s gr % Polyline n 7200 4425 m 7200 4575 l gs col0 s gr % Polyline n 7425 4500 m 7575 4500 l gs col0 s gr % Polyline n 7500 4425 m 7500 4575 l gs col0 s gr % Polyline n 7725 4500 m 7875 4500 l gs col0 s gr % Polyline n 7800 4425 m 7800 4575 l gs col0 s gr % Polyline n 2625 4200 m 2775 4200 l gs col0 s gr % Polyline n 2700 4125 m 2700 4275 l gs col0 s gr % Polyline n 2925 4200 m 3075 4200 l gs col0 s gr % Polyline n 3000 4125 m 3000 4275 l gs col0 s gr % Polyline n 3225 4200 m 3375 4200 l gs col0 s gr % Polyline n 3300 4125 m 3300 4275 l gs col0 s gr % Polyline n 3525 4200 m 3675 4200 l gs col0 s gr % Polyline n 3600 4125 m 3600 4275 l gs col0 s gr % Polyline n 3825 4200 m 3975 4200 l gs col0 s gr % Polyline n 3900 4125 m 3900 4275 l gs col0 s gr % Polyline n 4125 4200 m 4275 4200 l gs col0 s gr % Polyline n 4200 4125 m 4200 4275 l gs col0 s gr % Polyline n 4425 4200 m 4575 4200 l gs col0 s gr % Polyline n 4500 4125 m 4500 4275 l gs col0 s gr % Polyline n 4725 4200 m 4875 4200 l gs col0 s gr % Polyline n 4800 4125 m 4800 4275 l gs col0 s gr % Polyline n 5025 4200 m 5175 4200 l gs col0 s gr % Polyline n 5100 4125 m 5100 4275 l gs col0 s gr % Polyline n 5325 4200 m 5475 4200 l gs col0 s gr % Polyline n 5400 4125 m 5400 4275 l gs col0 s gr % Polyline n 5625 4200 m 5775 4200 l gs col0 s gr % Polyline n 5700 4125 m 5700 4275 l gs col0 s gr % Polyline n 5925 4200 m 6075 4200 l gs col0 s gr % Polyline n 6000 4125 m 6000 4275 l gs col0 s gr % Polyline n 6225 4200 m 6375 4200 l gs col0 s gr % Polyline n 6300 4125 m 6300 4275 l gs col0 s gr % Polyline n 6525 4200 m 6675 4200 l gs col0 s gr % Polyline n 6600 4125 m 6600 4275 l gs col0 s gr % Polyline n 6825 4200 m 6975 4200 l gs col0 s gr % Polyline n 6900 4125 m 6900 4275 l gs col0 s gr % Polyline n 7125 4200 m 7275 4200 l gs col0 s gr % Polyline n 7200 4125 m 7200 4275 l gs col0 s gr % Polyline n 7425 4200 m 7575 4200 l gs col0 s gr % Polyline n 7500 4125 m 7500 4275 l gs col0 s gr % Polyline n 7725 4200 m 7875 4200 l gs col0 s gr % Polyline n 7800 4125 m 7800 4275 l gs col0 s gr % Polyline n 2625 3900 m 2775 3900 l gs col0 s gr % Polyline n 2700 3825 m 2700 3975 l gs col0 s gr % Polyline n 2925 3900 m 3075 3900 l gs col0 s gr % Polyline n 3000 3825 m 3000 3975 l gs col0 s gr % Polyline n 3225 3900 m 3375 3900 l gs col0 s gr % Polyline n 3300 3825 m 3300 3975 l gs col0 s gr % Polyline n 3525 3900 m 3675 3900 l gs col0 s gr % Polyline n 3600 3825 m 3600 3975 l gs col0 s gr % Polyline n 3825 3900 m 3975 3900 l gs col0 s gr % Polyline n 3900 3825 m 3900 3975 l gs col0 s gr % Polyline n 4125 3900 m 4275 3900 l gs col0 s gr % Polyline n 4200 3825 m 4200 3975 l gs col0 s gr % Polyline n 4425 3900 m 4575 3900 l gs col0 s gr % Polyline n 4500 3825 m 4500 3975 l gs col0 s gr % Polyline n 4725 3900 m 4875 3900 l gs col0 s gr % Polyline n 4800 3825 m 4800 3975 l gs col0 s gr % Polyline n 5025 3900 m 5175 3900 l gs col0 s gr % Polyline n 5100 3825 m 5100 3975 l gs col0 s gr % Polyline n 5325 3900 m 5475 3900 l gs col0 s gr % Polyline n 5400 3825 m 5400 3975 l gs col0 s gr % Polyline n 5625 3900 m 5775 3900 l gs col0 s gr % Polyline n 5700 3825 m 5700 3975 l gs col0 s gr % Polyline n 5925 3900 m 6075 3900 l gs col0 s gr % Polyline n 6000 3825 m 6000 3975 l gs col0 s gr % Polyline n 6225 3900 m 6375 3900 l gs col0 s gr % Polyline n 6300 3825 m 6300 3975 l gs col0 s gr % Polyline n 6525 3900 m 6675 3900 l gs col0 s gr % Polyline n 6600 3825 m 6600 3975 l gs col0 s gr % Polyline n 6825 3900 m 6975 3900 l gs col0 s gr % Polyline n 6900 3825 m 6900 3975 l gs col0 s gr % Polyline n 7425 3900 m 7575 3900 l gs col0 s gr % Polyline n 7500 3825 m 7500 3975 l gs col0 s gr % Polyline n 7725 3900 m 7875 3900 l gs col0 s gr % Polyline n 7800 3825 m 7800 3975 l gs col0 s gr % Polyline n 8025 3900 m 8175 3900 l gs col0 s gr % Polyline n 8100 3825 m 8100 3975 l gs col0 s gr % Polyline n 2625 3600 m 2775 3600 l gs col0 s gr % Polyline n 2700 3525 m 2700 3675 l gs col0 s gr % Polyline n 2925 3600 m 3075 3600 l gs col0 s gr % Polyline n 3000 3525 m 3000 3675 l gs col0 s gr % Polyline n 3225 3600 m 3375 3600 l gs col0 s gr % Polyline n 3300 3525 m 3300 3675 l gs col0 s gr % Polyline n 3525 3600 m 3675 3600 l gs col0 s gr % Polyline n 3600 3525 m 3600 3675 l gs col0 s gr % Polyline n 3825 3600 m 3975 3600 l gs col0 s gr % Polyline n 3900 3525 m 3900 3675 l gs col0 s gr % Polyline n 4425 3600 m 4575 3600 l gs col0 s gr % Polyline n 4500 3525 m 4500 3675 l gs col0 s gr % Polyline n 4725 3600 m 4875 3600 l gs col0 s gr % Polyline n 4800 3525 m 4800 3675 l gs col0 s gr % Polyline n 5025 3600 m 5175 3600 l gs col0 s gr % Polyline n 5100 3525 m 5100 3675 l gs col0 s gr % Polyline n 5325 3600 m 5475 3600 l gs col0 s gr % Polyline n 5400 3525 m 5400 3675 l gs col0 s gr % Polyline n 5625 3600 m 5775 3600 l gs col0 s gr % Polyline n 5700 3525 m 5700 3675 l gs col0 s gr % Polyline n 5925 3600 m 6075 3600 l gs col0 s gr % Polyline n 6000 3525 m 6000 3675 l gs col0 s gr % Polyline n 6225 3600 m 6375 3600 l gs col0 s gr % Polyline n 6300 3525 m 6300 3675 l gs col0 s gr % Polyline n 6525 3600 m 6675 3600 l gs col0 s gr % Polyline n 6600 3525 m 6600 3675 l gs col0 s gr % Polyline n 6825 3600 m 6975 3600 l gs col0 s gr % Polyline n 6900 3525 m 6900 3675 l gs col0 s gr % Polyline n 7125 3600 m 7275 3600 l gs col0 s gr % Polyline n 7200 3525 m 7200 3675 l gs col0 s gr % Polyline n 7725 3600 m 7875 3600 l gs col0 s gr % Polyline n 7800 3525 m 7800 3675 l gs col0 s gr % Polyline n 8025 3600 m 8175 3600 l gs col0 s gr % Polyline n 8100 3525 m 8100 3675 l gs col0 s gr % Polyline n 2625 3300 m 2775 3300 l gs col0 s gr % Polyline n 2700 3225 m 2700 3375 l gs col0 s gr % Polyline n 2925 3300 m 3075 3300 l gs col0 s gr % Polyline n 3000 3225 m 3000 3375 l gs col0 s gr % Polyline n 3225 3300 m 3375 3300 l gs col0 s gr % Polyline n 3300 3225 m 3300 3375 l gs col0 s gr % Polyline n 3525 3300 m 3675 3300 l gs col0 s gr % Polyline n 3600 3225 m 3600 3375 l gs col0 s gr % Polyline n 3825 3300 m 3975 3300 l gs col0 s gr % Polyline n 3900 3225 m 3900 3375 l gs col0 s gr % Polyline n 4125 3300 m 4275 3300 l gs col0 s gr % Polyline n 4200 3225 m 4200 3375 l gs col0 s gr % Polyline n 4425 3300 m 4575 3300 l gs col0 s gr % Polyline n 4500 3225 m 4500 3375 l gs col0 s gr % Polyline n 4725 3300 m 4875 3300 l gs col0 s gr % Polyline n 4800 3225 m 4800 3375 l gs col0 s gr % Polyline n 5025 3300 m 5175 3300 l gs col0 s gr % Polyline n 5100 3225 m 5100 3375 l gs col0 s gr % Polyline n 5325 3300 m 5475 3300 l gs col0 s gr % Polyline n 5400 3225 m 5400 3375 l gs col0 s gr % Polyline n 5625 3300 m 5775 3300 l gs col0 s gr % Polyline n 5700 3225 m 5700 3375 l gs col0 s gr % Polyline n 5925 3300 m 6075 3300 l gs col0 s gr % Polyline n 6000 3225 m 6000 3375 l gs col0 s gr % Polyline n 6225 3300 m 6375 3300 l gs col0 s gr % Polyline n 6300 3225 m 6300 3375 l gs col0 s gr % Polyline n 6525 3300 m 6675 3300 l gs col0 s gr % Polyline n 6600 3225 m 6600 3375 l gs col0 s gr % Polyline n 6825 3300 m 6975 3300 l gs col0 s gr % Polyline n 6900 3225 m 6900 3375 l gs col0 s gr % Polyline n 7125 3300 m 7275 3300 l gs col0 s gr % Polyline n 7200 3225 m 7200 3375 l gs col0 s gr % Polyline n 7425 3300 m 7575 3300 l gs col0 s gr % Polyline n 7500 3225 m 7500 3375 l gs col0 s gr % Polyline n 7725 3300 m 7875 3300 l gs col0 s gr % Polyline n 7800 3225 m 7800 3375 l gs col0 s gr % Polyline n 8025 3300 m 8175 3300 l gs col0 s gr % Polyline n 8100 3225 m 8100 3375 l gs col0 s gr % Polyline n 2625 3000 m 2775 3000 l gs col0 s gr % Polyline n 2700 2925 m 2700 3075 l gs col0 s gr % Polyline n 2925 3000 m 3075 3000 l gs col0 s gr % Polyline n 3000 2925 m 3000 3075 l gs col0 s gr % Polyline n 3525 3000 m 3675 3000 l gs col0 s gr % Polyline n 3600 2925 m 3600 3075 l gs col0 s gr % Polyline n 3825 3000 m 3975 3000 l gs col0 s gr % Polyline n 3900 2925 m 3900 3075 l gs col0 s gr % Polyline n 4125 3000 m 4275 3000 l gs col0 s gr % Polyline n 4200 2925 m 4200 3075 l gs col0 s gr % Polyline n 4425 3000 m 4575 3000 l gs col0 s gr % Polyline n 4500 2925 m 4500 3075 l gs col0 s gr % Polyline n 4725 3000 m 4875 3000 l gs col0 s gr % Polyline n 4800 2925 m 4800 3075 l gs col0 s gr % Polyline n 5025 3000 m 5175 3000 l gs col0 s gr % Polyline n 5100 2925 m 5100 3075 l gs col0 s gr % Polyline n 5325 3000 m 5475 3000 l gs col0 s gr % Polyline n 5400 2925 m 5400 3075 l gs col0 s gr % Polyline n 5625 3000 m 5775 3000 l gs col0 s gr % Polyline n 5700 2925 m 5700 3075 l gs col0 s gr % Polyline n 6225 3000 m 6375 3000 l gs col0 s gr % Polyline n 6300 2925 m 6300 3075 l gs col0 s gr % Polyline n 6525 3000 m 6675 3000 l gs col0 s gr % Polyline n 6600 2925 m 6600 3075 l gs col0 s gr % Polyline n 6825 3000 m 6975 3000 l gs col0 s gr % Polyline n 6900 2925 m 6900 3075 l gs col0 s gr % Polyline n 7125 3000 m 7275 3000 l gs col0 s gr % Polyline n 7200 2925 m 7200 3075 l gs col0 s gr % Polyline n 7425 3000 m 7575 3000 l gs col0 s gr % Polyline n 7500 2925 m 7500 3075 l gs col0 s gr % Polyline n 7725 3000 m 7875 3000 l gs col0 s gr % Polyline n 7800 2925 m 7800 3075 l gs col0 s gr % Polyline n 8025 3000 m 8175 3000 l gs col0 s gr % Polyline n 8100 2925 m 8100 3075 l gs col0 s gr % Polyline n 2625 2700 m 2775 2700 l gs col0 s gr % Polyline n 2700 2625 m 2700 2775 l gs col0 s gr % Polyline n 2925 2700 m 3075 2700 l gs col0 s gr % Polyline n 3000 2625 m 3000 2775 l gs col0 s gr % Polyline n 3225 2700 m 3375 2700 l gs col0 s gr % Polyline n 3300 2625 m 3300 2775 l gs col0 s gr % Polyline n 3525 2700 m 3675 2700 l gs col0 s gr % Polyline n 3600 2625 m 3600 2775 l gs col0 s gr % Polyline n 3825 2700 m 3975 2700 l gs col0 s gr % Polyline n 3900 2625 m 3900 2775 l gs col0 s gr % Polyline n 4125 2700 m 4275 2700 l gs col0 s gr % Polyline n 4200 2625 m 4200 2775 l gs col0 s gr % Polyline n 4425 2700 m 4575 2700 l gs col0 s gr % Polyline n 4500 2625 m 4500 2775 l gs col0 s gr % Polyline n 4725 2700 m 4875 2700 l gs col0 s gr % Polyline n 4800 2625 m 4800 2775 l gs col0 s gr % Polyline n 5025 2700 m 5175 2700 l gs col0 s gr % Polyline n 5100 2625 m 5100 2775 l gs col0 s gr % Polyline n 5325 2700 m 5475 2700 l gs col0 s gr % Polyline n 5400 2625 m 5400 2775 l gs col0 s gr % Polyline n 5625 2700 m 5775 2700 l gs col0 s gr % Polyline n 5700 2625 m 5700 2775 l gs col0 s gr % Polyline n 6225 2700 m 6375 2700 l gs col0 s gr % Polyline n 6300 2625 m 6300 2775 l gs col0 s gr % Polyline n 6525 2700 m 6675 2700 l gs col0 s gr % Polyline n 6600 2625 m 6600 2775 l gs col0 s gr % Polyline n 6825 2700 m 6975 2700 l gs col0 s gr % Polyline n 6900 2625 m 6900 2775 l gs col0 s gr % Polyline n 7125 2700 m 7275 2700 l gs col0 s gr % Polyline n 7200 2625 m 7200 2775 l gs col0 s gr % Polyline n 7425 2700 m 7575 2700 l gs col0 s gr % Polyline n 7500 2625 m 7500 2775 l gs col0 s gr % Polyline n 7725 2700 m 7875 2700 l gs col0 s gr % Polyline n 7800 2625 m 7800 2775 l gs col0 s gr % Polyline n 8025 2700 m 8175 2700 l gs col0 s gr % Polyline n 8100 2625 m 8100 2775 l gs col0 s gr % Polyline n 2625 2400 m 2775 2400 l gs col0 s gr % Polyline n 2700 2325 m 2700 2475 l gs col0 s gr % Polyline n 2925 2400 m 3075 2400 l gs col0 s gr % Polyline n 3000 2325 m 3000 2475 l gs col0 s gr % Polyline n 3225 2400 m 3375 2400 l gs col0 s gr % Polyline n 3300 2325 m 3300 2475 l gs col0 s gr % Polyline n 3525 2400 m 3675 2400 l gs col0 s gr % Polyline n 3600 2325 m 3600 2475 l gs col0 s gr % Polyline n 3825 2400 m 3975 2400 l gs col0 s gr % Polyline n 3900 2325 m 3900 2475 l gs col0 s gr % Polyline n 4125 2400 m 4275 2400 l gs col0 s gr % Polyline n 4200 2325 m 4200 2475 l gs col0 s gr % Polyline n 4425 2400 m 4575 2400 l gs col0 s gr % Polyline n 4500 2325 m 4500 2475 l gs col0 s gr % Polyline n 4725 2400 m 4875 2400 l gs col0 s gr % Polyline n 4800 2325 m 4800 2475 l gs col0 s gr % Polyline n 5025 2400 m 5175 2400 l gs col0 s gr % Polyline n 5100 2325 m 5100 2475 l gs col0 s gr % Polyline n 5325 2400 m 5475 2400 l gs col0 s gr % Polyline n 5400 2325 m 5400 2475 l gs col0 s gr % Polyline n 5625 2400 m 5775 2400 l gs col0 s gr % Polyline n 5700 2325 m 5700 2475 l gs col0 s gr % Polyline n 5925 2400 m 6075 2400 l gs col0 s gr % Polyline n 6000 2325 m 6000 2475 l gs col0 s gr % Polyline n 6225 2400 m 6375 2400 l gs col0 s gr % Polyline n 6300 2325 m 6300 2475 l gs col0 s gr % Polyline n 6525 2400 m 6675 2400 l gs col0 s gr % Polyline n 6600 2325 m 6600 2475 l gs col0 s gr % Polyline n 6825 2400 m 6975 2400 l gs col0 s gr % Polyline n 6900 2325 m 6900 2475 l gs col0 s gr % Polyline n 7125 2400 m 7275 2400 l gs col0 s gr % Polyline n 7200 2325 m 7200 2475 l gs col0 s gr % Polyline n 7425 2400 m 7575 2400 l gs col0 s gr % Polyline n 7500 2325 m 7500 2475 l gs col0 s gr % Polyline n 7725 2400 m 7875 2400 l gs col0 s gr % Polyline n 7800 2325 m 7800 2475 l gs col0 s gr % Polyline n 8025 2400 m 8175 2400 l gs col0 s gr % Polyline n 8100 2325 m 8100 2475 l gs col0 s gr % Polyline n 2625 2100 m 2775 2100 l gs col0 s gr % Polyline n 2700 2025 m 2700 2175 l gs col0 s gr % Polyline n 2925 2100 m 3075 2100 l gs col0 s gr % Polyline n 3000 2025 m 3000 2175 l gs col0 s gr % Polyline n 3225 2100 m 3375 2100 l gs col0 s gr % Polyline n 3300 2025 m 3300 2175 l gs col0 s gr % Polyline n 3525 2100 m 3675 2100 l gs col0 s gr % Polyline n 3600 2025 m 3600 2175 l gs col0 s gr % Polyline n 3825 2100 m 3975 2100 l gs col0 s gr % Polyline n 3900 2025 m 3900 2175 l gs col0 s gr % Polyline n 4125 2100 m 4275 2100 l gs col0 s gr % Polyline n 4200 2025 m 4200 2175 l gs col0 s gr % Polyline n 4425 2100 m 4575 2100 l gs col0 s gr % Polyline n 4500 2025 m 4500 2175 l gs col0 s gr % Polyline n 4725 2100 m 4875 2100 l gs col0 s gr % Polyline n 4800 2025 m 4800 2175 l gs col0 s gr % Polyline n 5025 2100 m 5175 2100 l gs col0 s gr % Polyline n 5100 2025 m 5100 2175 l gs col0 s gr % Polyline n 5325 2100 m 5475 2100 l gs col0 s gr % Polyline n 5400 2025 m 5400 2175 l gs col0 s gr % Polyline n 5625 2100 m 5775 2100 l gs col0 s gr % Polyline n 5700 2025 m 5700 2175 l gs col0 s gr % Polyline n 5925 2100 m 6075 2100 l gs col0 s gr % Polyline n 6000 2025 m 6000 2175 l gs col0 s gr % Polyline n 6225 2100 m 6375 2100 l gs col0 s gr % Polyline n 6300 2025 m 6300 2175 l gs col0 s gr % Polyline n 6525 2100 m 6675 2100 l gs col0 s gr % Polyline n 6600 2025 m 6600 2175 l gs col0 s gr % Polyline n 6825 2100 m 6975 2100 l gs col0 s gr % Polyline n 6900 2025 m 6900 2175 l gs col0 s gr % Polyline n 7125 2100 m 7275 2100 l gs col0 s gr % Polyline n 7200 2025 m 7200 2175 l gs col0 s gr % Polyline n 7425 2100 m 7575 2100 l gs col0 s gr % Polyline n 7500 2025 m 7500 2175 l gs col0 s gr % Polyline n 7725 2100 m 7875 2100 l gs col0 s gr % Polyline n 7800 2025 m 7800 2175 l gs col0 s gr % Polyline n 8025 2100 m 8175 2100 l gs col0 s gr % Polyline n 8100 2025 m 8100 2175 l gs col0 s gr % Polyline n 2625 1800 m 2775 1800 l gs col0 s gr % Polyline n 2700 1725 m 2700 1875 l gs col0 s gr % Polyline n 2925 1800 m 3075 1800 l gs col0 s gr % Polyline n 3000 1725 m 3000 1875 l gs col0 s gr % Polyline n 3225 1800 m 3375 1800 l gs col0 s gr % Polyline n 3300 1725 m 3300 1875 l gs col0 s gr % Polyline n 3525 1800 m 3675 1800 l gs col0 s gr % Polyline n 3600 1725 m 3600 1875 l gs col0 s gr % Polyline n 3825 1800 m 3975 1800 l gs col0 s gr % Polyline n 3900 1725 m 3900 1875 l gs col0 s gr % Polyline n 4725 1800 m 4875 1800 l gs col0 s gr % Polyline n 4800 1725 m 4800 1875 l gs col0 s gr % Polyline n 5025 1800 m 5175 1800 l gs col0 s gr % Polyline n 5100 1725 m 5100 1875 l gs col0 s gr % Polyline n 5325 1800 m 5475 1800 l gs col0 s gr % Polyline n 5400 1725 m 5400 1875 l gs col0 s gr % Polyline n 5625 1800 m 5775 1800 l gs col0 s gr % Polyline n 5700 1725 m 5700 1875 l gs col0 s gr % Polyline n 5925 1800 m 6075 1800 l gs col0 s gr % Polyline n 6000 1725 m 6000 1875 l gs col0 s gr % Polyline n 6225 1800 m 6375 1800 l gs col0 s gr % Polyline n 6300 1725 m 6300 1875 l gs col0 s gr % Polyline n 6825 1800 m 6975 1800 l gs col0 s gr % Polyline n 6900 1725 m 6900 1875 l gs col0 s gr % Polyline n 7125 1800 m 7275 1800 l gs col0 s gr % Polyline n 7200 1725 m 7200 1875 l gs col0 s gr % Polyline n 7425 1800 m 7575 1800 l gs col0 s gr % Polyline n 7500 1725 m 7500 1875 l gs col0 s gr % Polyline n 7725 1800 m 7875 1800 l gs col0 s gr % Polyline n 7800 1725 m 7800 1875 l gs col0 s gr % Polyline n 8025 1800 m 8175 1800 l gs col0 s gr % Polyline n 8100 1725 m 8100 1875 l gs col0 s gr % Polyline n 2625 1500 m 2775 1500 l gs col0 s gr % Polyline n 2700 1425 m 2700 1575 l gs col0 s gr % Polyline n 2925 1500 m 3075 1500 l gs col0 s gr % Polyline n 3000 1425 m 3000 1575 l gs col0 s gr % Polyline n 3225 1500 m 3375 1500 l gs col0 s gr % Polyline n 3300 1425 m 3300 1575 l gs col0 s gr % Polyline n 3525 1500 m 3675 1500 l gs col0 s gr % Polyline n 3600 1425 m 3600 1575 l gs col0 s gr % Polyline n 3825 1500 m 3975 1500 l gs col0 s gr % Polyline n 3900 1425 m 3900 1575 l gs col0 s gr % Polyline n 4125 1500 m 4275 1500 l gs col0 s gr % Polyline n 4200 1425 m 4200 1575 l gs col0 s gr % Polyline n 4425 1500 m 4575 1500 l gs col0 s gr % Polyline n 4500 1425 m 4500 1575 l gs col0 s gr % Polyline n 4725 1500 m 4875 1500 l gs col0 s gr % Polyline n 4800 1425 m 4800 1575 l gs col0 s gr % Polyline n 5025 1500 m 5175 1500 l gs col0 s gr % Polyline n 5100 1425 m 5100 1575 l gs col0 s gr % Polyline n 5325 1500 m 5475 1500 l gs col0 s gr % Polyline n 5400 1425 m 5400 1575 l gs col0 s gr % Polyline n 5625 1500 m 5775 1500 l gs col0 s gr % Polyline n 5700 1425 m 5700 1575 l gs col0 s gr % Polyline n 5925 1500 m 6075 1500 l gs col0 s gr % Polyline n 6000 1425 m 6000 1575 l gs col0 s gr % Polyline n 6225 1500 m 6375 1500 l gs col0 s gr % Polyline n 6300 1425 m 6300 1575 l gs col0 s gr % Polyline n 6525 1500 m 6675 1500 l gs col0 s gr % Polyline n 6600 1425 m 6600 1575 l gs col0 s gr % Polyline n 6825 1500 m 6975 1500 l gs col0 s gr % Polyline n 6900 1425 m 6900 1575 l gs col0 s gr % Polyline n 7125 1500 m 7275 1500 l gs col0 s gr % Polyline n 7200 1425 m 7200 1575 l gs col0 s gr % Polyline n 7425 1500 m 7575 1500 l gs col0 s gr % Polyline n 7500 1425 m 7500 1575 l gs col0 s gr % Polyline n 8025 1500 m 8175 1500 l gs col0 s gr % Polyline n 8100 1425 m 8100 1575 l gs col0 s gr % Polyline n 5925 3000 m 6075 3000 l gs col0 s gr % Polyline n 6000 2925 m 6000 3075 l gs col0 s gr % Polyline n 2925 6900 m 3075 6900 l gs col0 s gr % Polyline n 3225 6900 m 3375 6900 l gs col0 s gr % Polyline n 3525 6900 m 3675 6900 l gs col0 s gr % Polyline n 3525 6600 m 3675 6600 l gs col0 s gr % Polyline n 3225 6300 m 3375 6300 l gs col0 s gr % Polyline n 3825 6300 m 3975 6300 l gs col0 s gr % Polyline n 3825 6600 m 3975 6600 l gs col0 s gr % Polyline n 4125 6900 m 4275 6900 l gs col0 s gr % Polyline n 4425 6900 m 4575 6900 l gs col0 s gr % Polyline n 4425 6600 m 4575 6600 l gs col0 s gr % Polyline n 4425 6300 m 4575 6300 l gs col0 s gr % Polyline n 4125 6300 m 4275 6300 l gs col0 s gr % Polyline n 4725 6300 m 4875 6300 l gs col0 s gr % Polyline n 5025 6300 m 5175 6300 l gs col0 s gr % Polyline n 5025 6600 m 5175 6600 l gs col0 s gr % Polyline n 5025 6900 m 5175 6900 l gs col0 s gr % Polyline n 4725 6900 m 4875 6900 l gs col0 s gr % Polyline n 5325 5700 m 5475 5700 l gs col0 s gr % Polyline n 5325 6000 m 5475 6000 l gs col0 s gr % Polyline n 5625 5700 m 5775 5700 l gs col0 s gr % Polyline n 5625 6000 m 5775 6000 l gs col0 s gr % Polyline n 5925 6000 m 6075 6000 l gs col0 s gr % Polyline n 6225 6000 m 6375 6000 l gs col0 s gr % Polyline n 6525 6300 m 6675 6300 l gs col0 s gr % Polyline n 5925 6300 m 6075 6300 l gs col0 s gr % Polyline n 6825 6300 m 6975 6300 l gs col0 s gr % Polyline n 7125 6300 m 7275 6300 l gs col0 s gr % Polyline n 7725 6600 m 7875 6600 l gs col0 s gr % Polyline n 7425 6600 m 7575 6600 l gs col0 s gr % Polyline n 7125 6600 m 7275 6600 l gs col0 s gr % Polyline n 6450 6600 m 6600 6600 l gs col0 s gr % Polyline n 6150 6600 m 6300 6600 l gs col0 s gr % Polyline n 5925 6600 m 6075 6600 l gs col0 s gr % Polyline n 5625 6600 m 5775 6600 l gs col0 s gr % Polyline n 5325 6600 m 5475 6600 l gs col0 s gr % Polyline n 6525 6900 m 6675 6900 l gs col0 s gr % Polyline n 6825 6900 m 6975 6900 l gs col0 s gr % Polyline n 7125 6900 m 7275 6900 l gs col0 s gr % Polyline n 7725 6900 m 7875 6900 l gs col0 s gr % Polyline n 8025 6900 m 8175 6900 l gs col0 s gr % Polyline n 4725 5100 m 4875 5100 l gs col0 s gr % Polyline n 5625 4500 m 5775 4500 l gs col0 s gr % Polyline n 5925 4500 m 6075 4500 l gs col0 s gr % Polyline n 7425 5400 m 7575 5400 l gs col0 s gr % Polyline n 8025 4500 m 8175 4500 l gs col0 s gr % Polyline n 8025 4200 m 8175 4200 l gs col0 s gr % Polyline n 7125 3900 m 7275 3900 l gs col0 s gr % Polyline n 7425 3600 m 7575 3600 l gs col0 s gr % Polyline n 5925 2700 m 6075 2700 l gs col0 s gr % Polyline n 6525 1800 m 6675 1800 l gs col0 s gr % Polyline n 4425 1800 m 4575 1800 l gs col0 s gr % Polyline n 4125 1800 m 4275 1800 l gs col0 s gr % Polyline n 3225 3000 m 3375 3000 l gs col0 s gr % Polyline n 4125 3600 m 4275 3600 l gs col0 s gr % Polyline n 3225 4800 m 3375 4800 l gs col0 s gr % Polyline n 3825 5700 m 3975 5700 l gs col0 s gr % Polyline n 5925 6900 m 6075 6900 l gs col0 s gr % Polyline n 5625 6900 m 5775 6900 l gs col0 s gr % Polyline n 6825 5100 m 6975 5100 l gs col0 s gr % Polyline n 2550 1350 m 8250 1350 l 8250 7050 l 2550 7050 l cp gs col0 s gr % Polyline 30.000 slw n 2400 7050 m 2850 7050 l 2850 6750 l 3450 6750 l 3450 6150 l 3150 6150 l 3150 6450 l 3750 6450 l 3750 6150 l 5850 6150 l 5850 6450 l 5250 6450 l 5250 5550 l 5850 5550 l 5850 5850 l 6450 5850 l 6450 6150 l 7350 6150 l 7350 6450 l 7950 6450 l 7950 6750 l 8250 6750 l 8250 7050 l 8400 7050 l gs col0 s gr % Polyline 7.500 slw n 7425 6000 m 7575 6000 l gs col0 s gr $F2psEnd rs %%EndDocument @endspecial 515 1686 a(Figure)21 b(1:)34 b(P)n(art)20 b(of)i(the)g(op)r(en)g(con)n(tour)e FA(\015)5 b FB(\()p FA(\033)s FB(\))23 b(\(b)r(old)f(line\),)i(and)d(the)h(set)g(\003)2849 1656 y Fv(\000)2905 1686 y FB(\()p FA(\033)s FB(\))h(\(shaded\).)p Black 515 1945 a(a)33 b(la)n(y)n(er)e(of)i Fy(\000)g FB(phase)g(along)f(the)h(b)r(ottom)h(w)n(all.)53 b(It)34 b(is)f(w)n(ell-kno)n(wn)e([1,)i(21)o(])h(that)f(there)515 2045 y(is)j(a)g(critical)f(v)-5 b(alue)36 b FA(h)1241 2057 y Fz(w)1295 2045 y FB(\()p FA(\014)t FB(\))i FA(>)f FB(0)f(of)g FA(h)g FB(at)g(whic)n(h)g(a)g(w)n(etting)g(transition)g(o)r (ccurs.)62 b(F)-7 b(or)515 2144 y FA(h)26 b(<)h(h)729 2156 y Fz(w)782 2144 y FB(\()p FA(\014)t FB(\),)32 b(the)e(la)n(y)n(er) e(has)h(a)h(\014nite)g(thic)n(kness)g(\(see)f([26)o(]\),)i(while)f(for) g FA(h)c Fy(\025)h FA(h)3041 2156 y Fz(w)3094 2144 y FB(\()p FA(\014)t FB(\),)32 b(the)515 2244 y(width)c(of)f(the)g(\014lm) h(of)f Fy(\000)g FB(phase)g(b)r(ecomes)g(macroscopic)e(\(of)i(order)f FA(N)2784 2214 y Fx(1)p Fz(=)p Fx(2)2888 2244 y FB(\))i(\(this)g(can)f (b)r(e)515 2344 y(pro)n(v)n(ed,)g(for)h(example,)h(along)f(the)h(line)g (of)f(the)i(argumen)n(t)d(leading)h(to)h(\(2.8\))f(b)r(elo)n(w\).)41 b(It)515 2443 y(is)26 b(actually)f(exp)r(ected)h(that)h(in)f(this)g (regime,)g(once)f(suitably)h(rescaled,)f(the)i(microscopic)515 2543 y(in)n(terface)i(con)n(v)n(erges)e(to)i(Bro)n(wnian)f(excursion;)i (the)g(sk)n(etc)n(h)e(pro)r(of)h(of)h(suc)n(h)f(a)g(result)h(in)515 2642 y(the)e(case)e FA(h)d FB(=)g(1)k(can)g(b)r(e)h(found)g(in)g([19)o (].)639 2742 y(Let)41 b(us)f(no)n(w)g(c)n(ho)r(ose)f(some)h FA(h)k Fy(\025)g FA(h)1852 2754 y Fz(w)1906 2742 y FB(\()p FA(\014)t FB(\))d(and)f(let)h FA(\025)k(>)f FB(0.)75 b(Our)40 b(second)f(result)515 2842 y(describ)r(es)26 b(the)i(b)r(eha)n(vior)e(of)h(the)h(\014lm)f(of)g Fy(\000)g FB(phase)g(as)g FA(\025)c Fy(!)g FB(0)2490 2812 y Fx(+)2545 2842 y FB(.)37 b(There)26 b(is)h(no)g(canonical)515 2941 y(w)n(a)n(y)j(of)i(measuring)f(the)h(width)g(of)g(the)g(\014lm)g(of)g Fy(\000)g FB(phase)f(in)h(the)g(Ising)f(mo)r(del,)j(or,)e(for)515 3041 y(that)c(matter,)f(ev)n(en)g(to)h(de\014ne)f(the)h(\014lm)g (itself.)38 b(W)-7 b(e)28 b(pro)r(ceed)f(as)g(follo)n(ws.)639 3141 y(Giv)n(en)k(a)f(con\014guration)f FA(\033)34 b FB(in)d(the)g(b)r(o)n(x)f(\003)2008 3153 y Fz(N)2071 3141 y FB(,)h(construct)f(its)h(extension)k(\026)-47 b FA(\033)35 b FB(to)30 b Fq(Z)3223 3110 y Fx(2)3291 3141 y FB(b)n(y)515 3240 y(setting,)36 b(for)e FA(x)h Fy(62)g FB(\003)1183 3252 y Fz(N)1246 3240 y FB(,)40 b(\026)-46 b FA(\033)1352 3252 y Fz(x)1429 3240 y FB(=)34 b Fy(\000)p FB(1)g(if)h FA(x)1799 3252 y Fx(2)1871 3240 y FA(<)f FB(0)g(and)39 b(\026)-47 b FA(\033)2261 3252 y Fz(x)2338 3240 y FB(=)34 b(1)h(otherwise.)56 b(Then)35 b(in)g(the)515 3340 y(con\014guration)k(\026)-47 b FA(\033)40 b FB(there)c(is)f(a)h(single)g(\(in\014nite\))h(op)r(en)f(P)n(eierls)f (con)n(tour.)61 b(This)36 b(P)n(eierls)515 3439 y(con)n(tour)d(can)h (in)n(tersect)g(itself,)j(and)e(w)n(e)f(use)g(the)h(deformation)f (rules)g(giv)n(en)g(in)h(Fig.)f(5)515 3539 y(to)d(turn)i(it)f(in)n(to)f (a)h(simple)g(curv)n(e.)49 b(W)-7 b(e)32 b(call)g(the)g(resulting)f(op) r(en)h(con)n(tour)f FA(\015)5 b FB(\()p FA(\033)s FB(\).)50 b(This)515 3639 y(con)n(tour)19 b(splits)h Fq(Z)1075 3609 y Fx(2)1133 3639 y FB(in)n(to)f(t)n(w)n(o)h(comp)r(onen)n(ts.)34 b(W)-7 b(e)20 b(denote)g(b)n(y)g(\003)2491 3609 y Fv(\000)2547 3639 y FB(\()p FA(\033)s FB(\))h(the)f(set)g(of)g(all)g(sites)g(of)515 3738 y(\003)573 3750 y Fz(N)661 3738 y FB(lying)k(\\b)r(elo)n(w")g FA(\015)5 b FB(\()p FA(\033)s FB(\),)26 b(see)f(Fig.)g(1.)36 b(The)25 b(v)n(olume)f(of)h(\003)2391 3708 y Fv(\000)2447 3738 y FB(\()p FA(\033)s FB(\))h(is)f(one)g(of)g(the)g(measures)515 3838 y(of)f(the)g(size)g(of)g(the)h(la)n(y)n(er)d(w)n(e)i(use.)36 b(The)24 b(other)f(one)h(is)g Fy(j)p FA(C)2318 3808 y Fv(\000)2374 3838 y FB(\()p FA(\033)s FB(\))p Fy(j)p FB(,)i(where)e FA(C)2862 3808 y Fv(\000)2918 3838 y FB(\()p FA(\033)s FB(\))i(is)e(the)g(set)515 3938 y(of)j(all)h(sites)f(in)h (\003)1065 3907 y Fv(\000)1121 3938 y FB(\()p FA(\033)s FB(\))g(connected)g(to)f(the)h(b)r(ottom)g(w)n(all)f(b)n(y)g(a)g(path)h (of)g Fy(\000)f FB(spins)g(in)h FA(\033)s FB(.)639 4037 y(Our)f(result)g(is)h(the)g(follo)n(wing)p Black 515 4193 a Fp(Theorem)j(5)p Black 41 w Fo(L)l(et)37 b FA(\014)i(>)c(\014) 1393 4205 y Fz(c)1464 4193 y Fo(and)i FA(h)e Fy(\025)g FA(h)1863 4205 y Fz(w)1917 4193 y FB(\()p FA(\014)t FB(\))p Fo(.)60 b(Ther)l(e)37 b(exist)f FA(\025)2610 4205 y Fx(0)2684 4193 y FA(>)f FB(0)p Fo(,)j FA(K)j(<)35 b Fy(1)p Fo(,)j(and)515 4292 y FA(C)574 4304 y Fx(2)634 4292 y FA(>)23 b FB(0)29 b Fo(such)h(that,)g(for)h(al)t(l)g FB(0)22 b FA(<)h(\025)g(<)g(\025) 1788 4304 y Fx(0)1855 4292 y Fo(and)31 b FA(N)g(>)23 b(K)6 b(\025)2328 4262 y Fv(\000)p Fx(2)p Fz(=)p Fx(3)2484 4292 y Fy(j)14 b FB(log)g FA(\025)p Fy(j)2713 4262 y Fx(3)2751 4292 y Fo(,)923 4482 y FA(\026)973 4494 y Fz(\014)s(;\025;h;) p Fx(\003)1197 4502 y Fu(N)1254 4482 y FB(\()p Fy(j)p FB(\003)1367 4448 y Fv(\000)1423 4482 y Fy(j)24 b FA(<)e Fy(j)14 b FB(log)g FA(\025)p Fy(j)1786 4448 y Fv(\000)p Fx(3)1890 4482 y FA(\025)1938 4448 y Fv(\000)p Fx(1)p Fz(=)p Fx(3)2108 4482 y FA(N)9 b FB(\))23 b Fy(\024)g FA(e)2366 4448 y Fv(\000)p Fz(C)2466 4456 y Fm(2)2509 4448 y Fv(j)11 b Fx(log)h Fz(\025)p Fv(j)2696 4422 y Fm(2)2729 4448 y Fz(\025)2768 4422 y Fm(2)p Fu(=)p Fm(3)2870 4448 y Fz(N)2947 4482 y FA(;)238 b FB(\(1.3\))515 4651 y Fo(and)900 4751 y FA(\026)950 4763 y Fz(\014)s(;\025;h;)p Fx(\003)1174 4771 y Fu(N)1231 4751 y FB(\()p Fy(j)p FA(C)1351 4717 y Fv(\000)1408 4751 y Fy(j)23 b FA(>)g(K)c Fy(j)14 b FB(log)g FA(\025)p Fy(j)1861 4717 y Fx(2)1913 4751 y FA(\025)1961 4717 y Fv(\000)p Fx(1)p Fz(=)p Fx(3)2131 4751 y FA(N)9 b FB(\))23 b Fy(\024)g FA(e)2389 4717 y Fv(\000)p Fz(C)2489 4725 y Fm(2)2532 4717 y Fv(j)11 b Fx(log)h Fz(\025)p Fv(j)2719 4692 y Fm(2)2752 4717 y Fz(\025)2791 4692 y Fm(2)p Fu(=)p Fm(3)2893 4717 y Fz(N)2970 4751 y FA(:)215 b FB(\(1.4\))515 4907 y(W)-7 b(e)27 b(exp)r(ect)g(that) h(the)f(t)n(w)n(o)f(quan)n(tities)h Fy(j)p FB(\003)1861 4876 y Fv(\000)1917 4907 y Fy(j)g FB(and)g Fy(j)p FA(C)2216 4876 y Fv(\000)2272 4907 y FB(\()p FA(\033)s FB(\))p Fy(j)h FB(are)e(t)n(ypically)h(the)g(same,)g(up)515 5006 y(to)g(a)g(m)n(ultiplicativ)n(e)h(constan)n(t:)p Black Black eop end %%Page: 7 7 TeXDict begin 7 6 bop Black 515 232 a Fr(En)n(tropic)22 b(repulsion)g(in)f(external)h(\014eld;)g(v)n(ersion)f(from)g(July)g(3,) f(2003)1159 b FB(7)p Black Black 515 523 a Fp(Conjecture)32 b(1)p Black 41 w Fo(Ther)l(e)f(exists)e(a)h(c)l(onstant)f FA(c)23 b(>)g FB(0)29 b Fo(such)h(that)1353 706 y FB(lim)1315 759 y Fz(N)6 b Fv(!1)1520 706 y FA(\026)1570 718 y Fz(\014)s(;\025;h;)p Fx(\003)1794 726 y Fu(N)1851 706 y FB(\()p Fy(j)p FA(C)1971 671 y Fv(\000)2028 706 y Fy(j)23 b FA(>)g(c)p Fy(j)p FB(\003)2279 671 y Fv(\000)2334 706 y Fy(j)p FB(\))h(=)e(1)14 b FA(:)515 925 y FB(\(Of)36 b(course)e Fy(j)p FB(\003)1016 895 y Fv(\000)1072 925 y FB(\()p FA(\033)s FB(\))p Fy(j)j(\025)f(j)p FA(C)1435 895 y Fv(\000)1491 925 y FB(\()p FA(\033)s FB(\))p Fy(j)h FB(for)e(all)g FA(\033)s FB(.\))62 b(W)-7 b(e)36 b(w)n(ere)e(unable)i(to)f(pro)n(v)n(e)f(this)i(con-)515 1025 y(jecture.)60 b(The)35 b(di\016cult)n(y)g(is)h(that)f(the)h (system)f(can)g(create)f(big)h(droplets)g(of)g(+)g(phase)515 1124 y(inside)f(the)h(la)n(y)n(er)d(of)j Fy(\000)f FB(phase,)h(and)f (it)h(seems)f(that)h(a)f(rather)f(complicated)h(metasta-)515 1224 y(bilit)n(y)g(analysis)f(is)h(required.)55 b(Suc)n(h)34 b(an)g(analysis)f(is)h(w)n(ell)f(understo)r(o)r(d)h(in)g(the)h(case)e (of)515 1323 y(regular)g(macroscopic)g(b)r(o)n(xes,)i(see)g(e.g.)f ([28].)58 b(Ho)n(w)n(ev)n(er,)35 b(w)n(e)g(are)e(here)i(in)g(a)f (situation)515 1423 y(where)27 b(the)h(b)r(o)n(x)f(is)g(random,)g(and)h (v)n(ery)e(anisotropic.)p Black 515 1606 a Fp(Remark)32 b(3)p Black 41 w Fo(The)c(lo)l(garithmic)h(c)l(orr)l(e)l(ctions)f(pr)l (esent)f(in)g(The)l(or)l(em)i(5)e(ar)l(e)h(arti\014cial)g(and)515 1705 y(should)h(b)l(e)g(r)l(emove)l(d.)39 b(The)29 b(r)l(e)l(ason)g(of) g(their)g(app)l(e)l(ar)l(anc)l(e)h(is)e(the)h(lack)g(of)h(lo)l(c)l(al)f (CL)-6 b(T)29 b(typ)l(e)515 1805 y(r)l(esults)23 b(for)h(Ising)g(r)l (andom-lines)h(in)e(the)h(vicinity)h(of)g(the)f(b)l(oundary)g(of)h(the) f(system.)36 b(Such)515 1905 y(estimates)e(have)i(b)l(e)l(en)e(pr)l (ove)l(d)h(in)g([11)q(])g(in)f(the)g(c)l(ase)h(of)g(r)l(andom-lines)g (in)g(the)f(bulk)h(but)515 2004 y(their)30 b(extension)f(se)l(ems)h (delic)l(ate.)515 2234 y Fp(Ac)m(kno)m(wledgmen)m(ts.)40 b FB(It)29 b(is)g(a)f(pleasure)g(to)g(thank)h(Ostap)f(Hryniv)h(for)f (man)n(y)g(fruitful)515 2334 y(discussions,)d(as)f(w)n(ell)i(as)e (useful)i(commen)n(ts)f(and)h(criticisms)f(on)g(earlier)f(v)n(ersions)f (of)j(this)515 2433 y(text.)35 b(The)22 b(author)e(is)i(also)e (grateful)h(to)g(W)-7 b(alter)22 b(Selk)n(e)f(for)g(bringing)f(his)i (atten)n(tion)f(to)h(the)515 2533 y(problem)30 b(of)g(in)n(terfacial)g (adsorption,)g(the)h(understanding)e(of)i(whic)n(h)f(w)n(as)g(the)h (original)515 2633 y(motiv)-5 b(ation)27 b(for)g(this)h(w)n(ork.)515 2907 y FD(2)134 b(Pro)t(ofs)515 3106 y FC(2.1)112 b(Pro)s(of)37 b(of)h(Theorem)g(1)f(and)i(its)e(corollary)515 3259 y Fp(2.1.1)93 b(Pro)s(of)32 b(of)g(Theorem)f(1)515 3412 y FB(Let)22 b FA(\027)5 b FB(\(2\))23 b(=)g(1)e(and)h FA(\027)5 b FB(\()p FA(d)p FB(\))24 b(=)f(1)p FA(=)p FB(2)d(when)i FA(d)i Fy(\025)e FB(3.)35 b(Theorem)21 b(1)g(is)h(a)g(rather)f(simple)h(corollary)515 3512 y(of)27 b(Theorem)g(2)g(and)h(the)g(follo)n(wing)e(result.)p Black 515 3678 a Fp(Lemma)31 b(1)h(\([16)o(],)f(Lemma)g(2.9\))p Black 41 w Fo(Ther)l(e)g(exists)e FA(K)g(>)22 b FB(0)29 b Fo(such)h(that,)g(for)h(al)t(l)g FA(\017)23 b(>)f FB(0)p Fo(,)678 3885 y FB(lim)640 3939 y Fz(N)6 b Fv(!1)845 3885 y FB(P)902 3897 y Fz(N)s(;)p Fx(+)p Fz(;)p Fx(0)1098 3793 y Fw(\020)1148 3790 y(\014)1148 3840 y(\014)1148 3890 y(\014)1176 3793 y(n)1231 3885 y FA(i)23 b Fy(2)g FB(\003)1419 3900 y Fx([)p Fz(N)q(=)p Fx(2])1618 3885 y FB(:)37 b FA(X)1747 3897 y Fz(i)1797 3885 y Fy(\024)23 b FA(K)6 b FB(\(log)14 b FA(N)9 b FB(\))2223 3851 y Fz(\027)t Fx(\()p Fz(d)p Fx(\))2351 3793 y Fw(o)2406 3790 y(\014)2406 3840 y(\014)2406 3890 y(\014)2457 3885 y Fy(\025)22 b FA(\017)p Fy(j)p FB(\003)2659 3900 y Fx([)p Fz(N)q(=)p Fx(2])2821 3885 y Fy(j)2844 3793 y Fw(\021)2917 3885 y FB(=)g(0)14 b FA(:)125 b FB(\(2.5\))639 4196 y(W)-7 b(e)28 b(\014rst)g(pro)n(v)n(e)e(a)h(lo)n(w)n(er)f(b)r(ound)i(on)f(the) h(partition)f(function.)p Black 515 4362 a Fp(Lemma)k(2)p Black 42 w Fo(Ther)l(e)h(exist)f FA(\025)1426 4374 y Fx(0)1489 4362 y FA(>)26 b FB(0)p Fo(,)31 b FA(r)e(>)c FB(0)31 b Fo(and)h FA(C)g(>)25 b FB(0)31 b Fo(such)g(that,)h(for)h(al)t (l)f FA(\025)26 b(<)g(\025)3179 4374 y Fx(0)3247 4362 y Fo(and)515 4461 y FA(N)32 b(>)22 b(\025)749 4431 y Fv(\000)p Fz(r)838 4461 y Fo(,)30 b(and)h(any)f(nonne)l(gative)g FA(\035)s Fo(,)1195 4659 y FA(Z)1252 4671 y Fz(N)s(;)p Fx(+)p Fz(;\025;\035)1522 4659 y Fy(\025)23 b FA(e)1649 4625 y Fv(\000)p Fz(C)14 b(\025)p Fl(V)q Fx(\()p Fv(j)e Fx(log)g Fz(\025)p Fv(j)2058 4600 y Fu(\027)s Fm(\()p Fu(d)p Fm(\))2170 4625 y Fx(\))g Fv(j)p Fx(\003)2273 4633 y Fu(N)2326 4625 y Fv(j)2364 4659 y FA(Z)2421 4671 y Fz(N)s(;)p Fx(+)p Fz(;)p Fx(0)p Fz(;\035)2676 4659 y FA(:)p Black Black eop end %%Page: 8 8 TeXDict begin 8 7 bop Black 515 232 a Fr(En)n(tropic)22 b(repulsion)g(in)f(external)h(\014eld;)g(v)n(ersion)f(from)g(July)g(3,) f(2003)1159 b FB(8)p Black 515 523 a Fp(Pro)s(of)23 b(of)g(Lemma)f(2.) 68 b FB(First)20 b(observ)n(e)f(that)h(it)g(is)g(enough)f(to)h(pro)n(v) n(e)f(the)h(corresp)r(onding)515 623 y(claim)27 b(without)h(pinning.)37 b(Indeed,)28 b(b)n(y)f(FK)n(G,)1195 773 y FA(Z)1252 785 y Fz(N)s(;)p Fx(+)p Fz(;\025;\035)p 1195 810 305 4 v 1198 886 a FA(Z)1255 898 y Fz(N)s(;)p Fx(+)p Fz(;)p Fx(0)p Fz(;\035)1533 829 y FB(=)22 b Fy(h)p FA(e)1691 795 y Fv(\000)p Fz(\025)1794 752 y Fk(P)1864 814 y Fu(i)1901 795 y Fl(V)q Fx(\()p Fz(X)2023 803 y Fu(i)2050 795 y Fx(\))2080 829 y Fy(i)2112 841 y Fz(N)s(;)p Fx(+)p Fz(;\035)1533 1056 y Fy(\025)g(h)p FA(e)1691 1022 y Fv(\000)p Fz(\025)1794 978 y Fk(P)1864 1041 y Fu(i)1901 1022 y Fl(V)q Fx(\()p Fz(X)2023 1030 y Fu(i)2050 1022 y Fx(\))2080 1056 y Fy(i)2112 1068 y Fz(N)s(;)p Fx(+)p Fz(;)p Fx(0)2318 1056 y FB(=)2416 1000 y FA(Z)2473 1012 y Fz(N)s(;)p Fx(+)p Fz(;\025)p 2416 1037 246 4 v 2419 1113 a FA(Z)2476 1125 y Fz(N)s(;)p Fx(+)p Fz(;)p Fx(0)2685 1056 y FA(:)515 1271 y FB(Let)27 b(no)n(w)1238 1398 y Fy(H)d FB(=)1420 1303 y Fw(\014)1420 1353 y(\014)1420 1402 y(\014)1447 1398 y FB(log)1568 1306 y Fw(\020)1618 1398 y FA(\025)p Ft(V)q FB(\()p Fy(j)14 b FB(log)h FA(\025)p Fy(j)1984 1364 y Fz(\027)t Fx(\()p Fz(d)p Fx(\))2112 1398 y FB(\))2144 1306 y Fw(\021)2208 1398 y FA(=c)2286 1410 y Fv(\000)2342 1398 y FB(\()p FA(d)p FB(\))2449 1303 y Fw(\014)2449 1353 y(\014)2449 1402 y(\014)2477 1323 y Fz(\027)t Fx(\()p Fz(d)p Fx(\))2633 1398 y FA(;)515 1564 y FB(where)27 b FA(c)791 1576 y Fv(\000)847 1564 y FB(\()p FA(d)p FB(\))h(has)f(b)r(een)h(in)n(tro)r (duced)g(in)g(Theorem)e(2)h(and)h FA(\027)5 b FB(\()p FA(d)p FB(\))29 b(is)e(de\014ned)h(ab)r(o)n(v)n(e.)888 1733 y FA(Z)945 1745 y Fz(N)s(;)p Fx(+)p Fz(;\025)1157 1733 y Fy(\025)23 b FA(e)1284 1699 y Fv(\000)p Fz(\025)p Fv(j)p Fx(\003)1440 1707 y Fu(N)1493 1699 y Fv(j)p Fl(V)q Fx(\(2)p Fv(H)p Fx(\))1724 1733 y FA(Z)1781 1745 y Fz(N)s(;)p Fx(0)1916 1733 y FB(P)1973 1745 y Fz(N)s(;)p Fx(0)2085 1733 y FB(\(0)g Fy(\024)f FA(X)2338 1745 y Fz(i)2389 1733 y Fy(\024)g FB(2)p Fy(H)q FA(;)27 b Fy(8)p FA(i)c Fy(2)h FB(\003)2874 1745 y Fz(N)2936 1733 y FB(\))14 b FA(;)515 1902 y FB(Ob)n(viously)-7 b(,)23 b(shifting)i(the)g(b)r (oundary)e(condition)h(from)g(0)g(to)g Fy(H)h FB(and)f(c)n(hanging)f(v) -5 b(ariables,)515 2002 y(w)n(e)27 b(can)g(write,)h(thanks)f(to)g(the)h (con)n(v)n(exit)n(y)e(of)i Ft(U)p FB(,)687 2184 y(P)744 2196 y Fz(N)s(;)p Fx(0)856 2184 y FB(\(0)23 b Fy(\024)g FA(X)1110 2196 y Fz(i)1160 2184 y Fy(\024)g FB(2)p Fy(H)q FA(;)k Fy(8)p FA(i)c Fy(2)g FB(\003)1645 2196 y Fz(N)1708 2184 y FB(\))g Fy(\025)g FA(e)1890 2150 y Fv(\000)p Fz(C)t Fv(H)2051 2125 y Fm(2)2093 2150 y Fz(N)2152 2125 y Fu(d)p Fn(\000)p Fm(1)2265 2184 y FB(P)2322 2196 y Fz(N)s(;)p Fx(0)2433 2184 y FB(\()p Fy(j)p FA(X)2557 2196 y Fz(i)2585 2184 y Fy(j)g(\024)g(H)q FA(;)k Fy(8)p FA(i)c Fy(2)h FB(\003)3075 2196 y Fz(N)3137 2184 y FB(\))14 b FA(:)515 2353 y FB(Applying)27 b(Theorem)g(2,)h(w)n(e)f(get)g(that)1040 2556 y FA(Z)1097 2568 y Fz(N)s(;)p Fx(+)p Fz(;\025)1309 2556 y Fy(\025)22 b FA(e)1435 2521 y Fv(\000)p Fx(\()p Fz(\025)p Fl(V)q Fx(\(2)p Fv(H)p Fx(\)+)p Fz(e)1818 2495 y Fn(\000)p Fu(c)1890 2508 y Fn(\000)1940 2495 y(H)1990 2478 y(\000)p Fu(\027)s Fm(\()p Fu(d)p Fm(\))2151 2521 y Fx(+)p Fz(c)p Fv(H)2289 2496 y Fm(2)2321 2521 y Fz(N)2380 2496 y Fn(\000)p Fm(1)2457 2521 y Fx(\))p Fv(j)p Fx(\003)2548 2529 y Fu(N)2601 2521 y Fv(j)2648 2556 y FA(Z)2705 2568 y Fz(N)s(;)p Fx(0)2831 2556 y FA(:)515 2725 y FB(Making)27 b(use)g(of)h(the)g(gro)n(wth)e(condition)h(on)g Ft(V)q FB(,)i(the)f(claim)f(follo)n(ws.)p 2759 2725 42 42 v 639 2869 a(Using)h(the)g(con)n(v)n(exit)n(y)e(of)h Ft(U)p FB(,)h(the)g(lemma)f(immediately)h(implies)g(that)722 3108 y(P)779 3120 y Fz(N)s(;)p Fx(+)p Fz(;\025;\035)1040 2966 y Fw( )1129 3029 y(X)1106 3207 y Fz(i)p Fv(2)p Fx(\003)1219 3215 y Fu(N)1287 3108 y FA(X)1356 3120 y Fz(i)1406 3108 y Fy(\025)23 b FA(\016)1534 3074 y Fv(\000)p Fx(1)1623 3108 y Fy(j)14 b FB(log)g FA(\025)p Fy(j)1852 3074 y Fz(\027)t Fx(\()p Fz(d)p Fx(\))1994 3108 y Fy(j)p FB(\003)2075 3120 y Fz(N)2138 3108 y Fy(j)2161 2966 y Fw(!)1049 3402 y Fy(\024)23 b FB(P)1194 3414 y Fz(N)s(;)p Fx(+)p Fz(;\025;\035)1455 3260 y Fw( )1544 3323 y(X)1521 3502 y Fz(i)p Fv(2)p Fx(\003)1634 3510 y Fu(N)1701 3402 y Ft(V)q FB(\()p FA(X)1858 3414 y Fz(i)1887 3402 y FB(\))g Fy(\025)g Ft(V)2100 3310 y Fw(\020)2150 3402 y FA(\016)2190 3368 y Fv(\000)p Fx(1)2279 3402 y Fy(j)14 b FB(log)g FA(\025)p Fy(j)2508 3368 y Fz(\027)t Fx(\()p Fz(d)p Fx(\))2636 3310 y Fw(\021)2713 3402 y Fy(j)p FB(\003)2794 3414 y Fz(N)2857 3402 y Fy(j)2880 3260 y Fw(!)1049 3664 y Fy(\024)23 b FB(exp)1278 3572 y Fw(n)1333 3664 y Fy(\000)p FA(\025)p Ft(V)1516 3572 y Fw(\020)1566 3664 y FA(\016)1606 3630 y Fv(\000)p Fx(1)1695 3664 y Fy(j)14 b FB(log)g FA(\025)p Fy(j)1924 3630 y Fz(\027)t Fx(\()p Fz(d)p Fx(\))2052 3572 y Fw(\021)2129 3664 y Fy(j)p FB(\003)2210 3676 y Fz(N)2273 3664 y Fy(j)2296 3572 y Fw(o)2402 3608 y FA(Z)2459 3620 y Fz(N)s(;)p Fx(+)p Fz(;)p Fx(0)p 2398 3645 246 4 v 2398 3721 a FA(Z)2455 3733 y Fz(N)s(;)p Fx(+)p Fz(;\025)1049 3874 y Fy(\024)23 b FB(exp)1278 3781 y Fw(n)1333 3874 y Fy(\000)p FA(\025)1460 3781 y Fw(\020)1509 3874 y Ft(V)1580 3781 y Fw(\020)1629 3874 y FA(\016)1669 3839 y Fv(\000)p Fx(1)1758 3874 y Fy(j)14 b FB(log)g FA(\025)p Fy(j)1987 3839 y Fz(\027)t Fx(\()p Fz(d)p Fx(\))2116 3781 y Fw(\021)2184 3874 y Fy(\000)k FA(C)i Ft(V)2416 3781 y Fw(\020)2466 3874 y Fy(j)14 b FB(log)g FA(\025)p Fy(j)2695 3839 y Fz(\027)t Fx(\()p Fz(d)p Fx(\))2823 3781 y Fw(\021)o(\021)2950 3874 y Fy(j)p FB(\003)3031 3886 y Fz(N)3093 3874 y Fy(j)3116 3781 y Fw(o)1049 4056 y Fy(\024)23 b FB(exp)1278 3964 y Fw(n)1333 4056 y Fy(\000)p FA(\025)p Ft(V)q FB(\()p Fy(j)14 b FB(log)h FA(\025)p Fy(j)1764 4022 y Fz(\027)t Fx(\()p Fz(d)p Fx(\))1892 4056 y FB(\))1938 3989 y Fw(\000)1976 4056 y FA(\016)2016 4022 y Fv(\000)p Fx(1)2124 4056 y Fy(\000)j FA(C)6 b FB(\))2304 3989 y Fw(\001)2370 4056 y Fy(j)p FB(\003)2451 4068 y Fz(N)2514 4056 y Fy(j)2537 3964 y Fw(o)2620 4056 y FA(;)515 4246 y FB(and)27 b(one)g(half)h(of)g (Theorem)e(1)i(is)f(pro)n(v)n(ed.)639 4345 y(Let)38 b(us)f(consider)f (the)i(second)e(half.)66 b(W)-7 b(e)38 b(\014rst)f(apply)g(Lemma)g(2)g (to)g(remo)n(v)n(e)f(the)515 4445 y(external)27 b(\014eld,)598 4651 y(P)655 4663 y Fz(N)s(;)p Fx(+)p Fz(;\025;\035)902 4651 y FB(\()958 4572 y Fw(X)934 4750 y Fz(i)p Fv(2)p Fx(\003)1047 4758 y Fu(N)1115 4651 y FA(X)1184 4663 y Fz(i)1235 4651 y Fy(\024)22 b FA(\016)s Fy(j)14 b FB(log)g FA(\025)p Fy(j)1591 4617 y Fz(\027)t Fx(\()p Fz(d)p Fx(\))1720 4651 y FB(\))1473 4890 y Fy(\024)23 b FA(e)1600 4856 y Fz(C)t(\025)p Fv(j)11 b Fx(log)h Fz(\025)p Fv(j)1878 4831 y Fu(\027)s Fm(\()p Fu(d)p Fm(\))1990 4856 y Fz(N)2049 4831 y Fu(d)2111 4890 y FB(P)2168 4902 y Fz(N)s(;)p Fx(+)p Fz(;)p Fx(0)p Fz(;\035)2409 4890 y FB(\()2465 4811 y Fw(X)2441 4990 y Fz(i)p Fv(2)p Fx(\003)2554 4998 y Fu(N)2622 4890 y FA(X)2691 4902 y Fz(i)2742 4890 y Fy(\024)23 b FA(\016)s Fy(j)14 b FB(log)g FA(\025)p Fy(j)3099 4856 y Fz(\027)t Fx(\()p Fz(d)p Fx(\))3227 4890 y FB(\))g FA(:)p Black Black eop end %%Page: 9 9 TeXDict begin 9 8 bop Black 515 232 a Fr(En)n(tropic)22 b(repulsion)g(in)f(external)h(\014eld;)g(v)n(ersion)f(from)g(July)g(3,) f(2003)1159 b FB(9)p Black 515 537 a(Let)23 b FA(R)h FB(=)f FA(R)897 549 y Fx(0)945 537 y Fy(\001)978 470 y Fw(\000)1016 537 y FA(\025)p Ft(V)q FB(\()p Fy(j)14 b FB(log)h FA(\025)p Fy(j)1382 507 y Fz(\027)t Fx(\()p Fz(d)p Fx(\))1511 537 y FB(\))1543 470 y Fw(\001)1581 484 y Fv(\000)p Fx(1)p Fz(=d)1739 537 y FB(,)24 b(with)g FA(R)2034 549 y Fx(0)2095 537 y FA(>)e FB(0)h(some)g(small)h(enough)f (real)f(n)n(um)n(b)r(er)515 636 y(to)27 b(b)r(e)h(c)n(hosen)f(b)r(elo)n (w.)36 b(Let)28 b(also)754 796 y(\001)823 808 y Fz(R)901 796 y FB(=)22 b Fy(f)p FA(x)h Fy(2)h Fq(Z)1234 762 y Fz(d)1310 796 y FB(:)37 b FA(x)1417 808 y Fz(i)1468 796 y Fy(\021)22 b FB(0)83 b(mo)r(d)28 b(2\()p FA(R)19 b FB(+)f(1\))p FA(;)41 b FB(for)27 b(some)g FA(i)c Fy(2)g(f)p FB(1)p FA(;)14 b(:)g(:)g(:)f(;)h(d)p Fy(gg)g FA(:)515 956 y FB(Using)19 b(the)i(usual)e(expansion)g(on)h(the)g(pinned)h (sites)f(\(see)f(e.g.)h([8]\))g(and)g(FK)n(G)f(inequalities,)515 1056 y(w)n(e)27 b(can)g(write)515 1216 y(P)572 1228 y Fz(N)s(;)p Fx(+)p Fz(;)p Fx(0)p Fz(;\035)813 1149 y Fw(\000)874 1137 y(X)851 1315 y Fz(i)p Fv(2)p Fx(\003)964 1323 y Fu(N)1032 1216 y FA(X)1101 1228 y Fz(i)1151 1216 y Fy(\024)c FA(\016)s Fy(j)14 b FB(log)g FA(\025)p Fy(j)1508 1182 y Fz(\027)t Fx(\()p Fz(d)p Fx(\))1636 1216 y Fy(j)p FB(\003)1717 1228 y Fz(N)1780 1216 y Fy(j)1803 1149 y Fw(\001)836 1452 y FB(=)964 1373 y Fw(X)923 1551 y Fz(A)p Fv(\032)p Fx(\003)1070 1559 y Fu(N)1138 1452 y FA(\027)1179 1464 y Fz(N)s(;)p Fx(+)p Fz(;\035)1368 1452 y FB(\()p FA(A)p FB(\))g(P)1565 1464 y Fz(A)1615 1448 y Fu(c)1646 1464 y Fz(;)p Fx(+)p Fz(;)p Fx(0)1773 1385 y Fw(\000)1835 1373 y(X)1811 1551 y Fz(i)p Fv(2)p Fx(\003)1924 1559 y Fu(N)1992 1452 y FA(X)2061 1464 y Fz(i)2112 1452 y Fy(\024)22 b FA(\016)s Fy(j)14 b FB(log)g FA(\025)p Fy(j)2468 1418 y Fz(\027)t Fx(\()p Fz(d)p Fx(\))2597 1452 y Fy(j)p FB(\003)2678 1464 y Fz(N)2740 1452 y Fy(j)2763 1385 y Fw(\001)836 1688 y Fy(\024)964 1610 y Fw(X)923 1788 y Fz(A)p Fv(\032)p Fx(\003)1070 1796 y Fu(N)1138 1688 y FA(\027)1179 1700 y Fz(N)s(;)p Fx(+)p Fz(;\035)1368 1688 y FB(\()p FA(A)p FB(\))g(P)1565 1700 y Fz(A)1615 1684 y Fu(c)1646 1700 y Fz(;)p Fx(+)p Fz(;)p Fx(0)1773 1621 y Fw(\000)1835 1610 y(X)1811 1788 y Fz(i)p Fv(2)p Fx(\003)1924 1796 y Fu(N)1992 1688 y FA(X)2061 1700 y Fz(i)2112 1688 y Fy(\024)22 b FA(\016)s Fy(j)14 b FB(log)g FA(\025)p Fy(j)2468 1654 y Fz(\027)t Fx(\()p Fz(d)p Fx(\))2597 1688 y Fy(j)p FB(\003)2678 1700 y Fz(N)2740 1688 y Fy(j)2800 1618 y Fw(\014)2800 1668 y(\014)2865 1688 y FA(X)29 b Fy(\021)23 b FB(0)k(on)g(\001)3304 1700 y Fz(R)3359 1621 y Fw(\001)3411 1688 y FA(;)515 1931 y FB(where)g FA(\027)796 1943 y Fz(N)s(;)p Fx(+)p Fz(;\035)1012 1931 y FB(is)h(the)g(induced)g (probabilit)n(y)e(measure)h(on)g(the)h(subsets)f(of)h(\003)2994 1943 y Fz(N)3057 1931 y FB(.)639 2030 y(The)33 b(grid)e(\001)1059 2042 y Fz(R)1146 2030 y FB(splits)h(\003)1426 2042 y Fz(N)1521 2030 y FB(in)n(to)g FA(M)40 b FB(=)30 b Fy(j)p FB(\003)1991 2042 y Fz(N)2054 2030 y Fy(j)p FA(=)p FB(\(2)p FA(R)22 b FB(+)f(2\))2438 2000 y Fz(d)2509 2030 y FB(cubic)32 b(cells)g(of)g(sidelength)515 2130 y(2)p FA(R)20 b FB(+)h(1.)46 b(\(T)-7 b(o)30 b(simplify)i(the)f(notation,)g(w)n(e)f(supp)r(ose)h (that)g(this)g(splitting)g(can)f(b)r(e)h(done)515 2230 y(exactly)-7 b(.\))35 b(Giv)n(en)24 b(a)f(realization)f FA(A)i FB(of)g(the)g(random)f(set)g(of)h(the)g(pinned)g(sites,)h(w)n(e) e(declare)515 2329 y(a)30 b(cell)g Fj(clean)f FB(if)i(it)g(do)r(es)f (not)g(con)n(tain)f(an)n(y)h(site)g(of)g FA(A)p FB(;)i(otherwise)d(it)i (is)f Fj(dirt)n(y)p FB(.)44 b(W)-7 b(e)31 b(need)515 2429 y(to)h(ensure)g(that,)i(for)d(all)h FA(\035)i Fy(2)d Ft(CW)r FB(,)j(at)e(least)g(half)g(of)h(the)f(cells)g(of)h(the)f(grid)g (are)f(clean.)515 2528 y(This)26 b(follo)n(ws)g(easily)f(from)h(the)h (\014rst)f(claim)h(of)f(Theorem)g(3)g(with)h FA(\017)22 b FB(=)2783 2496 y Fx(1)p 2783 2510 34 4 v 2783 2557 a(2)2826 2528 y FA(M)t(=)p Fy(j)p FB(\003)3034 2540 y Fz(N)3096 2528 y Fy(j)p FB(,)27 b(whic)n(h)515 2628 y(implies)j(that)h (at)f(least)f(one)h(half)g(of)h(the)f(cells)g(are)f(clean)h(once)g FA(N)39 b FB(is)30 b(large)f(enough,)h(up)515 2728 y(to)g(an)f(ev)n(en) n(t)h(of)g(probabilit)n(y)f FA(e)1521 2698 y Fv(\000)p Fz(c)10 b(M)1687 2728 y FB(.)44 b(In)30 b(the)h(rest)e(of)h(this)g(pro) r(of,)g(w)n(e)g(supp)r(ose)g FA(N)38 b FB(is)30 b(at)515 2827 y(least)d(that)h(large.)639 2927 y(Let)38 b(us)g(n)n(um)n(b)r(er)g (the)h(clean)e(cells)h(as)g Fy(C)1952 2939 y Fx(1)1989 2927 y FA(;)14 b(:)g(:)g(:)f(;)h Fy(C)2217 2939 y Fz(K)2281 2927 y FB(,)41 b FA(K)k Fy(\025)2577 2894 y Fx(1)p 2577 2908 V 2577 2956 a(2)2620 2927 y FA(M)9 b FB(,)40 b(and)e(let)g FA(Y)3123 2939 y Fz(k)3164 2927 y FB(,)j FA(k)i FB(=)515 3027 y(1)p FA(;)14 b(:)g(:)g(:)f(;)h(K)6 b FB(,)27 b(b)r(e)h(the)g (indicator)f(function)h(of)f(the)h(ev)n(en)n(t)1462 3120 y Fw(X)1451 3298 y Fz(i)p Fv(2C)1555 3307 y Fu(k)1606 3199 y FA(X)1675 3211 y Fz(i)1725 3199 y Fy(\024)23 b FB(4)p FA(\016)s Fy(j)14 b FB(log)f FA(\025)p Fy(j)2123 3164 y Fz(\027)t Fx(\()p Fz(d)p Fx(\))2275 3199 y Fy(jC)2342 3211 y Fz(k)2382 3199 y Fy(j)h FA(:)515 3446 y FB(W)-7 b(e)28 b(clearly)e(ha)n(v)n(e)h(the)h(inclusion)f(\(for)g(all)h FA(\025)g FB(small)f(enough\))1075 3620 y Fw(\010)1147 3608 y(X)1123 3786 y Fz(i)p Fv(2)p Fx(\003)1236 3794 y Fu(N)1304 3687 y FA(X)1373 3699 y Fz(i)1424 3687 y Fy(\024)22 b FA(\016)s Fy(j)14 b FB(log)g FA(\025)p Fy(j)1780 3653 y Fz(\027)t Fx(\()p Fz(d)p Fx(\))1909 3687 y Fy(j)p FB(\003)1990 3699 y Fz(N)2052 3687 y Fy(j)2075 3620 y Fw(\011)2147 3687 y Fy(\032)2234 3620 y Fw(\010)2313 3583 y Fz(K)2283 3608 y Fw(X)2283 3787 y Fz(k)q Fx(=1)2417 3687 y FA(Y)2465 3699 y Fz(i)2516 3687 y Fy(\025)2614 3654 y Fx(1)p 2614 3668 V 2614 3716 a(3)2657 3687 y FA(K)2734 3620 y Fw(\011)2796 3687 y FA(:)515 3934 y FB(No)n(w,)31 b(under)f(P)1026 3946 y Fz(A)1076 3930 y Fu(c)1106 3946 y Fz(;)p Fx(+)p Fz(;)p Fx(0)1234 3934 y FB(\()14 b Fy(\001)g(j)g FA(X)34 b Fy(\021)28 b FB(0)f(on)g(\001)1803 3946 y Fz(R)1858 3934 y FB(\),)32 b(the)f FA(Y)2139 3946 y Fz(i)2197 3934 y FB(are)f(i.i.d.)46 b(Bernoulli)29 b(random)h(v)-5 b(ari-)515 4033 y(ables.)36 b(Let)28 b(us)f(denote)h(their)f(common)g(la)n(w)g(b)n (y)h(Q)2139 4045 y Fz(R)2193 4033 y FB(.)37 b(Using)28 b(\(2.5\),)g(w)n(e)f(see)g(that)609 4218 y(Q)674 4230 y Fz(R)728 4218 y FB(\()p FA(Y)808 4230 y Fz(i)860 4218 y FB(=)22 b(1\))h Fy(\024)g FB(P)1189 4230 y Fz(R;)p Fx(+)p Fz(;)p Fx(0)1380 4126 y Fw(\020)1430 4123 y(\014)1430 4173 y(\014)1430 4222 y(\014)1457 4126 y(n)1513 4218 y FA(i)f Fy(2)i FB(\003)1701 4233 y Fx([)p Fz(R=)p Fx(2])1896 4218 y FB(:)37 b FA(X)2025 4230 y Fz(i)2076 4218 y Fy(\024)23 b FB(2)2206 4184 y Fz(d)p Fx(+3)2328 4218 y FA(\016)s Fy(j)14 b FB(log)g FA(\025)p Fy(j)2597 4184 y Fz(\027)t Fx(\()p Fz(d)p Fx(\))2725 4126 y Fw(o)2780 4123 y(\014)2780 4173 y(\014)2780 4222 y(\014)2831 4218 y Fy(\025)2929 4186 y Fx(1)p 2929 4200 V 2929 4247 a(2)2972 4218 y Fy(j)p FB(\003)3053 4233 y Fx([)p Fz(R=)p Fx(2])3212 4218 y Fy(j)3235 4126 y Fw(\021)1044 4375 y Fy(\024)23 b FB(1)p FA(=)p FB(10)14 b FA(;)515 4535 y FB(pro)n(vided)26 b FA(\016)s FB(,)i(and)f(then)i FA(\025)p FB(,)f(are)e(c)n(hosen)h(small) g(enough.)37 b(Consequen)n(tly)-7 b(,)1341 4772 y Fy(\012)1406 4737 y Fz(M)1406 4792 y(k)q Fx(=1)1531 4772 y FB(Q)1596 4784 y Fz(R)1650 4772 y FB(\()1707 4668 y Fz(M)1682 4693 y Fw(X)1682 4872 y Fz(k)q Fx(=1)1816 4772 y FA(Y)1864 4784 y Fz(i)1915 4772 y Fy(\025)2013 4739 y Fx(1)p 2013 4753 V 2013 4800 a(6)2056 4772 y FA(M)9 b FB(\))23 b Fy(\024)g FA(e)2328 4737 y Fv(\000)p Fz(C)14 b(M)2530 4772 y FA(;)515 5006 y FB(and)27 b(the)h(conclusion)f(follo)n(ws,)g (pro)n(vided)f(w)n(e)h(tak)n(e)g FA(R)2223 5018 y Fx(0)2288 5006 y FB(small)g(enough.)p Black Black eop end %%Page: 10 10 TeXDict begin 10 9 bop Black 515 232 a Fr(En)n(tropic)22 b(repulsion)g(in)f(external)h(\014eld;)g(v)n(ersion)f(from)g(July)g(3,) f(2003)1118 b FB(10)p Black 515 523 a Fp(2.1.2)93 b(Pro)s(of)32 b(of)g(Corollary)g(1)515 676 y FB(W)-7 b(e)37 b(only)f(giv)n(e)g(the)h (pro)r(of)f(for)g FA(d)i FB(=)g(2)e(since)g(the)h(argumen)n(t)f(for)g FA(d)i Fy(\025)g FB(3)e(is)g(iden)n(tical.)515 776 y(Notice)27 b(\014rst)h(that)g(it)g(is)f(enough)g(to)h(pro)n(v)n(e)d(the)j(result)g (for)f FA(X)2475 788 y Fx(0)2512 776 y FB(.)37 b(Indeed,)28 b(b)n(y)f(FK)n(G,)1386 958 y(E)1443 970 y Fz(N)s(;)p Fx(+)p Fz(;\025;\035)1691 958 y FB(\()p FA(X)1792 970 y Fz(i)1819 958 y FB(\))d Fy(\024)e FB(E)2019 970 y Fx(2)p Fz(N)s(;)p Fx(+)p Fz(;\025;\035)2300 958 y FB(\()p FA(X)2401 970 y Fx(0)2438 958 y FB(\))14 b FA(;)515 1139 y FB(for)27 b(all)g FA(i)c Fy(2)g FB(\003)945 1151 y Fz(N)1008 1139 y FB(,)28 b(while)f(for)g FA(i)c Fy(2)g FB(\003)1590 1151 y Fz(\017N)1708 1139 y FB(\(0)g FA(<)g(\017)g(<)f FB(1\))28 b(w)n(e)f(ha)n(v)n(e)f(that)1389 1321 y(E)1446 1333 y Fz(N)s(;)p Fx(+)p Fz(;\025;\035)1693 1321 y FB(\()p FA(X)1794 1333 y Fz(i)1822 1321 y FB(\))d Fy(\025)g FB(E)2022 1333 y Fz(\017N)s(;)p Fx(+)p Fz(;\025;\035)2297 1321 y FB(\()p FA(X)2398 1333 y Fx(0)2435 1321 y FB(\))14 b FA(;)515 1503 y FB(Theorem)27 b(1)g(implies)h(that)1204 1696 y(E)1261 1708 y Fz(N)s(;)p Fx(+)p Fz(;\025;\035)1508 1696 y FB(\()p Fy(j)p FB(\003)1621 1708 y Fz(N)1684 1696 y Fy(j)1707 1662 y Fv(\000)p Fx(1)1834 1618 y Fw(X)1810 1796 y Fz(i)p Fv(2)p Fx(\003)1923 1804 y Fu(N)1991 1696 y FA(X)2060 1708 y Fz(i)2087 1696 y FB(\))c Fy(2)f FB(\()p FA(a)2297 1708 y Fx(1)2335 1696 y FA(;)14 b(a)2416 1708 y Fx(2)2453 1696 y FB(\))p Fy(H)2555 1708 y Fz(\025;d)2667 1696 y FA(;)515 1960 y FB(for)30 b(some)h(constan)n(ts)e(0)g FA(<)f(a)1435 1972 y Fx(1)1501 1960 y FA(<)g(a)1638 1972 y Fx(2)1704 1960 y FA(<)g Fy(1)j FB(pro)n(vided)f FA(\025)h FB(is)g(small)g(enough)f(and)h FA(N)39 b FB(large)515 2060 y(enough.)d(Using)27 b(FK)n(G)h(inequalities,)f(w)n(e)g(deduce)h (that)627 2254 y Fy(j)p FB(\003)708 2266 y Fz(N)770 2254 y Fy(j)793 2219 y Fv(\000)p Fx(1)920 2175 y Fw(X)896 2353 y Fz(i)p Fv(2)p Fx(\003)1009 2361 y Fu(N)1077 2254 y FB(E)1134 2266 y Fz(N)s(;)p Fx(+)p Fz(;\025;\035)1381 2254 y FB(\()p FA(X)1482 2266 y Fz(i)1510 2254 y FB(\))23 b Fy(\024)g(j)p FB(\003)1734 2266 y Fz(N)1797 2254 y Fy(j)1820 2219 y Fv(\000)p Fx(1)1946 2175 y Fw(X)1923 2353 y Fz(i)p Fv(2)p Fx(\003)2036 2361 y Fu(N)2104 2254 y FB(E)2161 2266 y Fx(2)p Fz(N)s(;)p Fx(+)p Fz(;\025;\035)2441 2254 y FB(\()p FA(X)2542 2266 y Fx(0)2579 2254 y FB(\))h(=)e(E)2779 2266 y Fx(2)p Fz(N)s(;)p Fx(+)p Fz(;\025;\035)3060 2254 y FB(\()p FA(X)3161 2266 y Fx(0)3198 2254 y FB(\))14 b FA(;)515 2522 y FB(from)36 b(whic)n(h)g(it)i(follo)n(ws)d(that)i(E) 1586 2534 y Fz(N)s(;)p Fx(+)p Fz(;\025;\035)1833 2522 y FB(\()p FA(X)1934 2534 y Fx(0)1972 2522 y FB(\))h Fy(\025)f FA(a)2188 2534 y Fx(1)2226 2522 y Fy(H)2296 2534 y Fz(\025;d)2430 2522 y FB(for)f FA(N)46 b FB(large)35 b(enough.)63 b(The)515 2622 y(complemen)n(tary)26 b(b)r(ound)i(is)g(also)e(a)h(trivial)g (consequence)g(of)g(FK)n(G:)875 2816 y Fy(j)p FB(\003)956 2828 y Fz(N)1019 2816 y Fy(j)1042 2781 y Fv(\000)p Fx(1)1169 2737 y Fw(X)1145 2915 y Fz(i)p Fv(2)p Fx(\003)1258 2923 y Fu(N)1326 2816 y FB(E)1383 2828 y Fz(N)s(;)p Fx(+)p Fz(;\025;\035)1630 2816 y FB(\()p FA(X)1731 2828 y Fz(i)1759 2816 y FB(\))c Fy(\025)g(j)p FB(\003)1983 2828 y Fz(N)2046 2816 y Fy(j)2069 2781 y Fv(\000)p Fx(1)2239 2737 y Fw(X)2172 2915 y Fz(i)p Fv(2)p Fx(\003)2285 2926 y Fm([)p Fu(N=)p Fm(2])2440 2816 y FB(E)2497 2828 y Fz(N)s(;)p Fx(+)p Fz(;\025;\035)2745 2816 y FB(\()p FA(X)2846 2828 y Fz(i)2873 2816 y FB(\))1814 3065 y Fy(\025)g(j)p FB(\003)1983 3077 y Fz(N)2046 3065 y Fy(j)2069 3031 y Fv(\000)p Fx(1)2239 2986 y Fw(X)2172 3164 y Fz(i)p Fv(2)p Fx(\003)2285 3175 y Fm([)p Fu(N=)p Fm(2])2440 3065 y FB(E)2497 3080 y Fx([)p Fz(N)q(=)p Fx(2])p Fz(;)p Fx(+)p Fz(;\025;\035)2848 3065 y FB(\()p FA(X)2949 3077 y Fx(0)2986 3065 y FB(\))1814 3297 y(=)1912 3265 y Fx(1)p 1912 3279 34 4 v 1912 3326 a(4)1978 3297 y FB(E)2035 3312 y Fx([)p Fz(N)q(=)p Fx(2])p Fz(;)p Fx(+)p Fz(;\025;\035)2385 3297 y FB(\()p FA(X)2486 3309 y Fx(0)2524 3297 y FB(\))14 b FA(:)515 3479 y FB(This)27 b(sho)n(ws)g(that)h(E)1180 3491 y Fz(N)s(;)p Fx(+)p Fz(;\025;\035)1427 3479 y FB(\()p FA(X)1528 3491 y Fx(0)1565 3479 y FB(\))c Fy(\024)e FB(4)p FA(a)1794 3491 y Fx(2)1845 3479 y Fy(H)1915 3491 y Fz(\025;d)2013 3479 y FB(.)515 3711 y FC(2.2)112 b(Pro)s(of)37 b(of)h(Theorems)g(2,)g(3)f(and)h(4)515 3864 y Fp(Pro)s(of)31 b(of)h(Theorem)g(2.)73 b FB(W)-7 b(e)28 b(\014rst)f(establish)g(the)h(lo)n(w)n(er)e(b)r(ound.)37 b(W)-7 b(e)28 b(write)646 4046 y(P)703 4058 y Fz(N)766 4046 y FB(\()p Fy(j)p FA(X)890 4058 y Fz(i)917 4046 y Fy(j)23 b(\024)g FA(`;)k Fy(8)p FA(i)c Fy(2)h FB(\003)1371 4058 y Fz(N)1433 4046 y FB(\))g Fy(\025)e FB(P)1633 4058 y Fz(N)s(;)p Fx(+)1763 4046 y FB(\()p FA(X)1864 4058 y Fz(i)1915 4046 y Fy(\024)g FA(`;)28 b Fy(8)p FA(i)22 b Fy(2)i FB(\003)2322 4058 y Fz(N)2384 4046 y FB(\))14 b(P)2487 4058 y Fz(N)2550 4046 y FB(\()p FA(X)2651 4058 y Fz(i)2702 4046 y Fy(\025)22 b FB(0)p FA(;)28 b Fy(8)p FA(i)22 b Fy(2)i FB(\003)3116 4058 y Fz(N)3178 4046 y FB(\))14 b FA(:)515 4244 y FB(By)25 b([16)o(,)h(Theorem)e(3.1],)h(P) 1381 4256 y Fz(N)1444 4244 y FB(\()p FA(X)1545 4256 y Fz(i)1595 4244 y Fy(\025)e FB(0)p FA(;)k Fy(8)p FA(i)c Fy(2)g FB(\003)2009 4256 y Fz(N)2072 4244 y FB(\))g Fy(\025)g FA(e)2254 4214 y Fv(\000)p Fz(c)11 b(N)2406 4189 y Fu(d)p Fn(\000)p Fm(1)2543 4244 y FB(for)25 b(some)f FA(c)f(>)g FB(0)i(if)h FA(d)d Fy(\025)f FB(2,)515 4344 y(and)f(can)g(th)n(us)g(b)r (e)h(neglected.)35 b(Let)21 b(us)h(consider)e(the)i(other)f(one.)34 b(W)-7 b(e)22 b(in)n(tro)r(duce)f FA(R)j FB(=)e FA(e)3297 4314 y Fz(\024)11 b(`)515 4444 y FB(if)30 b FA(d)c FB(=)g(2,)j(and)g FA(R)e FB(=)f FA(e)1230 4413 y Fz(\024)10 b(`)1307 4388 y Fm(2)1373 4444 y FB(if)30 b FA(d)c Fy(\025)g FB(3,)k(where)e FA(\024)i FB(is)f(a)g(small)g(n)n(um)n(b)r(er)g(to)g(b)r(e)h(c)n(hosen) f(later,)515 4543 y(and)e(the)h(grid)754 4725 y(\001)823 4737 y Fz(R)901 4725 y FB(=)22 b Fy(f)p FA(x)h Fy(2)h Fq(Z)1234 4691 y Fz(d)1310 4725 y FB(:)37 b FA(x)1417 4737 y Fz(i)1468 4725 y Fy(\021)22 b FB(0)83 b(mo)r(d)28 b(2\()p FA(R)19 b FB(+)f(1\))p FA(;)41 b FB(for)27 b(some)g FA(i)c Fy(2)g(f)p FB(1)p FA(;)14 b(:)g(:)g(:)f(;)h(d)p Fy(gg)g FA(:)515 4907 y FB(This)29 b(grid)f(splits)i(\003)1156 4919 y Fz(N)1248 4907 y FB(in)n(to)f FA(M)34 b FB(=)26 b Fy(j)p FB(\003)1705 4919 y Fz(N)1767 4907 y Fy(j)p FA(=)p FB(\(2)p FA(R)20 b FB(+)f(2\))2147 4876 y Fz(d)2215 4907 y FB(cubic)29 b(cells)g(of)g(sidelength)h(2)p FA(R)19 b FB(+)g(1.)515 5006 y(\(T)-7 b(o)29 b(simplify)h(the)g(notation,)f(w)n (e)h(supp)r(ose)f(that)g(this)h(splitting)g(can)f(b)r(e)h(done)f (exactly)-7 b(.\))p Black Black eop end %%Page: 11 11 TeXDict begin 11 10 bop Black 515 232 a Fr(En)n(tropic)22 b(repulsion)g(in)f(external)h(\014eld;)g(v)n(ersion)f(from)g(July)g(3,) f(2003)1118 b FB(11)p Black 515 523 a(Denoting)32 b(b)n(y)h(P)1056 493 y Fz(t)1056 546 y(N)s(;)p Fx(+)1218 523 y FB(the)g(measure)e(with)i FA(t)g FB(b)r(oundary)f(conditions,)h(FK)n(G)f(inequalities)515 623 y(then)c(imply)g(that)679 798 y(P)736 810 y Fz(N)s(;)p Fx(+)866 798 y FB(\()p FA(X)967 810 y Fz(i)1018 798 y Fy(\024)22 b FA(`;)28 b Fy(8)p FA(i)23 b Fy(2)g FB(\003)1425 810 y Fz(N)1488 798 y FB(\))g Fy(\025)g FB(P)1688 764 y Fz(`)1688 819 y(N)s(;)p Fx(+)1817 798 y FB(\()p FA(X)1918 810 y Fz(i)1969 798 y Fy(\024)g FA(`;)k Fy(8)p FA(i)c Fy(2)g FB(\003)2376 810 y Fz(N)2453 798 y Fy(j)14 b FA(X)29 b Fy(\021)22 b FA(`)28 b FB(on)f(\001)2922 810 y Fz(R)2977 798 y FB(\))1543 945 y(=)c(\(P)1720 957 y Fz(R)1774 945 y FB(\()p FA(X)1875 957 y Fz(i)1926 945 y Fy(\025)f FB(0)p FA(;)27 b Fy(8)p FA(i)c Fy(2)h FB(\003)2340 957 y Fz(R)2408 945 y Fy(j)14 b FA(X)2514 957 y Fz(i)2564 945 y Fy(\024)23 b FA(`;)k Fy(8)p FA(i)c Fy(2)g FB(\003)2971 957 y Fz(R)3025 945 y FB(\)\))3090 903 y Fz(M)3191 945 y FA(:)515 1120 y FB(No)n(w,)598 1321 y(P)655 1333 y Fz(R)709 1321 y FB(\()p FA(X)810 1333 y Fz(i)860 1321 y Fy(\025)g FB(0)p FA(;)k Fy(8)p FA(i)c Fy(2)h FB(\003)1275 1333 y Fz(R)1343 1321 y Fy(j)14 b FA(X)1449 1333 y Fz(i)1499 1321 y Fy(\024)23 b FA(`;)k Fy(8)p FA(i)c Fy(2)g FB(\003)1906 1333 y Fz(R)1960 1321 y FB(\))1567 1445 y Fy(\025)g FB(P)1712 1457 y Fz(R;)p Fx(+)1837 1445 y FB(\()p FA(X)1938 1457 y Fz(i)1988 1445 y Fy(\024)g FA(`;)k Fy(8)p FA(i)c Fy(2)h FB(\003)2396 1457 y Fz(R)2450 1445 y FB(\))14 b(P)2553 1457 y Fz(R)2607 1445 y FB(\()p FA(X)2708 1457 y Fz(i)2759 1445 y Fy(\025)22 b FB(0)p FA(;)27 b Fy(8)p FA(i)c Fy(2)h FB(\003)3173 1457 y Fz(R)3227 1445 y FB(\))14 b FA(:)515 1621 y FB(As)27 b(ab)r(o)n(v)n(e,)1344 1734 y(P)1401 1746 y Fz(R)1455 1734 y FB(\()p FA(X)1556 1746 y Fz(i)1607 1734 y Fy(\025)c FB(0)p FA(;)k Fy(8)p FA(i)c Fy(2)g FB(\003)2021 1746 y Fz(R)2075 1734 y FB(\))h Fy(\025)e FA(e)2257 1699 y Fv(\000)p Fz(c)11 b(R)2400 1674 y Fu(d)p Fn(\000)p Fm(1)2526 1734 y FA(;)515 1879 y FB(while,)28 b(using)f([16)o(,)h(Corollary)d (2.6],)882 2054 y(P)939 2066 y Fz(R;)p Fx(+)1064 2054 y FB(\()p FA(X)1165 2066 y Fz(i)1215 2054 y Fy(\024)e FA(`;)k Fy(8)p FA(i)c Fy(2)h FB(\003)1623 2066 y Fz(R)1677 2054 y FB(\))f Fy(\025)g FB(1)18 b Fy(\000)g(j)p FB(\003)2044 2066 y Fz(R)2098 2054 y Fy(j)45 b FB(sup)2149 2124 y Fz(i)p Fv(2)p Fx(\003)2262 2132 y Fu(R)2323 2054 y FB(P)2380 2066 y Fz(R;)p Fx(+)2505 2054 y FB(\()p FA(X)2606 2066 y Fz(i)2657 2054 y FA(>)22 b(`)p FB(\))h Fy(\025)2932 2022 y Fx(1)p 2932 2036 34 4 v 2932 2083 a(2)2989 2054 y FA(;)515 2287 y FB(pro)n(vided)28 b(that)i FA(\024)g FB(is)f(c)n(hosen)g(small)g(enough,)h(and)f(then)h FA(`)f FB(large)g(enough)f(\(actually)i(the)515 2387 y(ab)r(o)n(v)n(e)g (reference)g(do)r(es)h(not)g(giv)n(e)g(explicitly)g(a)g(rate)g(of)g (con)n(v)n(ergence,)f(but)i(a)f(glance)f(at)515 2487 y(the)e(pro)r(of)f(sho)n(ws)f(that)i(sup)1418 2507 y Fz(i)p Fv(2)p Fx(\003)1531 2515 y Fu(R)1597 2487 y FB(P)1654 2499 y Fz(R;)p Fx(+)1778 2487 y FB(\()p FA(X)1879 2499 y Fz(i)1930 2487 y FA(>)23 b(`)p FB(\))g Fy(\024)f FA(R)2259 2456 y Fv(\000)p Fz(c)11 b(`)2384 2487 y FB(\).)639 2586 y(Collecting)27 b(all)h(the)g(estimates)f(pro)n(v)n(es)f(the)i(lo)n(w)n (er)e(b)r(ound.)639 2733 y(Let)j(us)f(no)n(w)g(turn)h(to)f(the)h(upp)r (er)f(b)r(ound.)40 b(\001)2100 2745 y Fz(R)2183 2733 y FB(is)29 b(the)g(same)f(grid)f(as)h(ab)r(o)n(v)n(e)f(\(for)h(an)515 2832 y FA(R)23 b FB(to)g(b)r(e)h(c)n(hosen)e(later\).)35 b(Then)23 b(it)g(follo)n(ws)f(from)h(con)n(v)n(exit)n(y)e(of)i Ft(U)g FB(and)g(FK)n(G)f(inequalities)515 2932 y(that)587 3108 y(P)644 3120 y Fz(N)707 3108 y FB(\()p Fy(j)p FA(X)831 3120 y Fz(i)858 3108 y Fy(j)h(\024)g FA(`;)k Fy(8)p FA(i)c Fy(2)h FB(\003)1312 3120 y Fz(N)1374 3108 y FB(\))g Fy(\024)e FB(P)1574 3120 y Fz(N)s(;)p Fx(+)1704 3108 y FB(\()p FA(X)1805 3120 y Fz(i)1856 3108 y Fy(\024)g FB(2)p FA(`;)27 b Fy(8)p FA(i)c Fy(2)g FB(\003)2304 3120 y Fz(N)2367 3108 y FB(\))14 b FA(e)2452 3073 y Fz(c`)2510 3048 y Fm(2)2553 3073 y Fv(j)p Fz(@)t Fx(\003)2657 3081 y Fu(N)2710 3073 y Fv(j)1430 3257 y Fy(\024)22 b FB(P)1574 3269 y Fz(N)s(;)p Fx(+)1704 3257 y FB(\()p FA(X)1805 3269 y Fz(i)1856 3257 y Fy(\024)g FB(2)p FA(`;)27 b Fy(8)p FA(i)c Fy(2)g FB(\003)2304 3269 y Fz(N)2381 3257 y Fy(j)14 b FA(X)29 b Fy(\021)23 b FB(0)k(on)g(\001)2857 3269 y Fz(R)2939 3257 y FB(\))14 b FA(e)3024 3222 y Fz(c`)3082 3197 y Fm(2)3125 3222 y Fv(j)p Fz(@)t Fx(\003)3229 3230 y Fu(N)3283 3222 y Fv(j)1430 3406 y FB(=)22 b(\(P)1606 3418 y Fz(R;)p Fx(+)1731 3406 y FB(\()p FA(X)1832 3418 y Fz(i)1883 3406 y Fy(\024)g FB(2)p FA(`;)27 b Fy(8)p FA(i)c Fy(2)h FB(\003)2332 3418 y Fz(R)2386 3406 y FB(\)\))2450 3364 y Fz(M)2552 3406 y FA(e)2591 3372 y Fz(c`)2649 3347 y Fm(2)2691 3372 y Fv(j)p Fz(@)t Fx(\003)2795 3380 y Fu(N)2849 3372 y Fv(j)2887 3406 y FA(:)515 3591 y FB(W)-7 b(e)33 b(c)n(ho)r(ose)f FA(R)i FB(as)e(follo)n(ws:)46 b(If)34 b FA(d)e FB(=)g(2,)i(then)f FA(R)g FB(=)e FA(e)2236 3560 y Fz(\032`)2302 3591 y FB(,)k(while)e(in)g (the)h(case)e FA(d)g Fy(\025)f FB(3,)j(w)n(e)515 3690 y(c)n(ho)r(ose)26 b FA(R)e FB(=)e FA(e)991 3660 y Fz(\032`)1053 3635 y Fm(2)1090 3690 y FB(,)28 b(with)g FA(\032)f FB(large)g(enough.) 36 b(Then)1377 3866 y(P)1434 3878 y Fz(R;)p Fx(+)1558 3866 y FB(\()p FA(X)1659 3878 y Fz(i)1710 3866 y Fy(\024)23 b FB(2)p FA(`;)j Fy(8)p FA(i)d Fy(2)h FB(\003)2159 3878 y Fz(R)2213 3866 y FB(\))f Fy(\024)g FB(1)p FA(=)p FB(2)14 b FA(;)515 4041 y FB(b)n(y)22 b(the)g(results)g(of)g([16])g(\(since)g (the)h(t)n(ypical)f(heigh)n(t)g(of)g(the)h(rep)r(elled)f(\014eld)h(is)f (prop)r(ortional)515 4141 y(to)27 b(\(log)15 b FA(R)q FB(\))866 4111 y Fz(\027)t Fx(\()p Fz(d)p Fx(\))1016 4141 y FB(=)23 b FA(\032)1147 4111 y Fz(\027)t Fx(\()p Fz(d)p Fx(\))1275 4141 y FA(`)p FB(\).)37 b(This)27 b(completes)g(the)h (pro)r(of.)p 2394 4141 42 42 v 515 4288 a Fp(Pro)s(of)j(of)h(Theorem)g (3.)515 4387 y Fo(First)e(statement.)38 b FB(Let)28 b Fy(A)h FB(b)r(e)f(the)h(\(random\))e(set)h(of)g(pinned)h(sites.)38 b(The)28 b(crucial)g(obser-)515 4487 y(v)-5 b(ation)27 b(is)h(that)1019 4663 y(E)1076 4675 y Fz(N)s(;)p Fx(+)p Fz(;)p Fx(0)p Fz(;\035)1331 4570 y Fw(\020)1381 4663 y FA(e)1420 4628 y Fz(t)p Fv(jAj)1541 4570 y Fw(\021)1614 4663 y FB(=)1742 4584 y Fw(X)1702 4762 y Fz(A)p Fv(\032)p Fx(\003)1849 4770 y Fu(N)1916 4663 y FA(e)1955 4628 y Fz(t)p Fv(j)p Fz(A)p Fv(j)2087 4663 y FA(\035)2135 4628 y Fv(j)p Fz(A)p Fv(j)2228 4663 y FB(Z)2279 4675 y Fz(A)2329 4658 y Fu(c)2360 4675 y Fz(;)p Fx(+)p Fz(;)p Fx(0)p Fz(;)p Fx(0)2541 4663 y FA(=)p FB(Z)2634 4675 y Fz(N)s(;)p Fx(+)p Fz(;)p Fx(0)p Fz(;\035)1614 4926 y FB(=)1712 4868 y(Z)1763 4882 y Fz(N)s(;)p Fx(+)p Fz(;)p Fx(0)p Fz(;e)1994 4865 y Fu(t)2020 4882 y Fz(\035)p 1712 4906 352 4 v 1741 4982 a FB(Z)1792 4994 y Fz(N)s(;)p Fx(+)p Fz(;)p Fx(0)p Fz(;\035)2087 4926 y FA(:)p Black Black eop end %%Page: 12 12 TeXDict begin 12 11 bop Black 515 232 a Fr(En)n(tropic)22 b(repulsion)g(in)f(external)h(\014eld;)g(v)n(ersion)f(from)g(July)g(3,) f(2003)1118 b FB(12)p Black 515 523 a(Therefore)26 b(an)h(application)g (of)h(the)g(exp)r(onen)n(tial)f(Cheb)n(yshev)g(inequalit)n(y)g(yields) 619 706 y(P)676 718 y Fz(N)s(;)p Fx(+)p Fz(;)p Fx(0)p Fz(;\035)931 706 y FB(\()p Fy(jAj)d FA(>)e(\020)6 b Fy(j)p FB(\003)1309 718 y Fz(N)1372 706 y Fy(j)p FB(\))24 b Fy(\024)e FA(e)1577 671 y Fv(\000)p Fz(t\020)t Fv(j)p Fx(\003)1753 679 y Fu(N)1806 671 y Fv(j)p Fx(+log)q(\(Z)2029 689 y Fu(N)r(;)p Fm(+)p Fu(;)p Fm(0)p Fu(;e)2232 677 y(t)2259 689 y(\035)2298 671 y Fz(=)p Fx(Z)2372 679 y Fu(N)r(;)p Fm(+)p Fu(;)p Fm(0)2531 671 y Fx(\))p Fv(\000)p Fx(log)q(\(Z)2761 679 y Fu(N)r(;)p Fm(+)p Fu(;)p Fm(0)p Fu(;\035)2974 671 y Fz(=)p Fx(Z)3048 679 y Fu(N)r(;)p Fm(+)p Fu(;)p Fm(0)3208 671 y Fx(\))3252 706 y FA(:)515 888 y FB(Cho)r(osing)k FA(t)h FB(suc)n(h)g(that)h FA(e)1340 858 y Fz(t)1392 888 y FB(=)1490 856 y Fx(1)p 1490 870 34 4 v 1490 917 a(2)1533 888 y FB(\()p FA(\035)21 b FB(+)c FA(\035)1758 900 y Fz(c)1792 888 y FB(\))28 b(and)f(using)h(\(1.2\),)f (w)n(e)g(get)g(the)h(conclusion,)f(for)515 988 y(all)g FA(N)32 b(>)22 b(N)883 1000 y Fx(0)920 988 y FB(\()p FA(\035)s(;)14 b(\020)6 b FB(\).)515 1088 y Fo(Se)l(c)l(ond)31 b(statement.)43 b FB(Since)30 b FA(\025)d FB(=)f(0)j(in)h(all)f(the)h (pro)r(of,)f(w)n(e)h(omit)f(it)i(from)e(the)h(notations.)515 1187 y(It)e(is)f(pro)n(v)n(ed)f(in)i([12)o(])g(that)g(the)g(condition)f FA(\035)f Fy(2)d Ft(CW)30 b FB(implies)e(that)1443 1370 y(lim)1405 1423 y Fz(N)6 b Fv(!1)1610 1370 y Fy(j)p FB(\003)1691 1382 y Fz(N)1754 1370 y Fy(j)1777 1336 y Fv(\000)p Fx(1)1889 1370 y Fq(E)1944 1382 y Fz(N)s(;)p Fx(+)p Fz(;\035)2147 1370 y FB([)p FA(\032)2213 1382 y Fz(N)2276 1370 y FB(])23 b(=)g(0)14 b FA(;)515 1585 y FB(where)20 b FA(\032)791 1597 y Fz(N)854 1585 y FB(\()p FA(X)7 b FB(\))23 b(=)1104 1523 y Fw(P)1192 1610 y Fz(i)p Fv(2)p Fx(\003)1305 1618 y Fu(N)1377 1585 y FB(1)1419 1600 y Fv(f)p Fz(X)1507 1608 y Fu(i)1533 1600 y Fx(=0)p Fv(g)1656 1585 y FB(.)34 b(So)21 b(there)f(exists)h(a)f(sequence)g FA(c)2685 1597 y Fz(N)2748 1585 y FB(,)i(with)g(lim)14 b FA(c)3141 1597 y Fz(N)3227 1585 y FB(=)22 b(0,)515 1685 y(suc)n(h)30 b(that)h Fq(E)943 1697 y Fz(N)s(;)p Fx(+)p Fz(;\035)1146 1685 y FB([)p FA(\032)1212 1697 y Fz(N)1275 1685 y FB(])e Fy(\024)f FA(c)1456 1697 y Fz(N)1533 1685 y Fy(j)p FB(\003)1614 1697 y Fz(N)1676 1685 y Fy(j)p FB(.)47 b(Let)31 b Fy(E)1965 1697 y Fz(N)2056 1685 y FB(=)d Fy(f)p FA(X)48 b FB(:)43 b FA(\032)2417 1697 y Fz(N)2480 1685 y FB(\()p FA(X)7 b FB(\))28 b Fy(\024)g FB(2)p FA(c)2819 1697 y Fz(N)2895 1685 y Fy(j)p FB(\003)2976 1697 y Fz(N)3039 1685 y Fy(jg)p FB(.)46 b(Using)515 1785 y(again)26 b(the)i(expansion)f(on)g(pinned)h (sites,)g(w)n(e)f(ha)n(v)n(e)f(the)i(follo)n(wing)636 2037 y Fq(E)691 2049 y Fz(N)s(;)p Fx(+)p Fz(;\035)894 1895 y Fw(")966 1958 y(X)942 2137 y Fz(i)p Fv(2)p Fx(\003)1055 2145 y Fu(N)1123 2037 y FA(X)1192 2049 y Fz(i)1220 1895 y Fw(#)1291 2037 y Fy(\025)23 b Fq(E)1434 2049 y Fz(N)s(;)p Fx(+)p Fz(;\035)1636 1895 y Fw(")1708 1958 y(X)1685 2137 y Fz(i)p Fv(2)p Fx(\003)1798 2145 y Fu(N)1866 2037 y FA(X)1935 2049 y Fz(i)1962 2037 y FB(1)2004 2049 y Fv(E)2040 2057 y Fu(N)2097 1895 y Fw(#)1291 2274 y FB(=)1516 2195 y Fw(X)1476 2373 y Fz(A)p Fv(\032)p Fx(\003)1623 2381 y Fu(N)1379 2433 y Fv(j)p Fz(A)p Fv(j\024)p Fx(2)p Fz(c)1584 2441 y Fu(N)1636 2433 y Fv(j)p Fx(\003)1701 2441 y Fu(N)1754 2433 y Fv(j)1788 2274 y FA(\027)1829 2286 y Fz(N)s(;)p Fx(+)p Fz(;\035)2018 2274 y FB(\()p FA(A)p FB(\))h Fq(E)2223 2286 y Fz(A)2273 2269 y Fu(c)2304 2286 y Fz(;)p Fx(+)p Fz(;)p Fx(0)2432 2274 y FB(\()2487 2195 y Fw(X)2464 2373 y Fz(i)p Fv(2)p Fx(\003)2577 2381 y Fu(N)2645 2274 y FA(X)2714 2286 y Fz(i)2741 2274 y FB(\))1291 2576 y Fy(\025)1516 2498 y Fw(X)1476 2676 y Fz(A)p Fv(\032)p Fx(\003)1623 2684 y Fu(N)1379 2736 y Fv(j)p Fz(A)p Fv(j\024)p Fx(2)p Fz(c)1584 2744 y Fu(N)1636 2736 y Fv(j)p Fx(\003)1701 2744 y Fu(N)1754 2736 y Fv(j)1788 2576 y FA(\027)1829 2588 y Fz(N)s(;)p Fx(+)p Fz(;\035)2018 2576 y FB(\()p FA(A)p FB(\))2327 2498 y Fw(X)2304 2676 y Fz(i)p Fv(2)p Fx(\003)2417 2684 y Fu(N)2181 2754 y Fz(d)p Fx(\()p Fz(x;A)p Fx(\))p Fv(\025)p Fz(c)2458 2724 y Fn(\000)p Fm(1)p Fu(=)p Fm(4)2458 2774 y Fu(N)2607 2576 y Fq(E)2662 2591 y Fz(B)2712 2627 y Fu(c)2739 2602 y Fn(\000)p Fm(1)p Fu(=)p Fm(4)2739 2649 y Fu(N)2880 2591 y Fx(\()p Fz(x)p Fx(\))p Fz(;)p Fx(+)p Fz(;)p Fx(0)3097 2576 y FB(\()p FA(X)3198 2588 y Fz(i)3225 2576 y FB(\))1291 2885 y Fy(\025)f FA(C)d Fy(j)14 b FB(log)g FA(c)1652 2897 y Fz(N)1715 2885 y Fy(j)g(j)p FB(\003)1833 2897 y Fz(N)1895 2885 y Fy(j)g FA(;)515 3067 y FB(where)28 b FA(B)819 3079 y Fz(r)856 3067 y FB(\()p FA(x)p FB(\))f(=)e Fy(f)p FA(y)42 b FB(:)e Fy(j)p FA(y)22 b Fy(\000)d FA(x)p Fy(j)26 b(\024)g FA(r)r Fy(g)p FB(,)k(and)f(w)n(e)g(used)g(p)r(ositivit)n(y)g(of)g(the)h (\014eld)f(and)g(FK)n(G)515 3167 y(inequalities;)37 b(the)e(last)e (inequalit)n(y)h(follo)n(ws)f(from)h(Mark)n(o)n(v)e(inequalit)n(y)i (and)g(the)g(usual)515 3278 y(en)n(tropic)23 b(repulsion)g(estimate)h (for)f(a)h(square)f(b)r(o)n(x)g(of)h(radius)f FA(c)2488 3235 y Fv(\000)p Fx(1)p Fz(=)p Fx(4)2488 3303 y Fz(N)2668 3278 y FB(with)i(0)e(b.c.,)i(see)f([16)o(].)639 3478 y(Since,)35 b(when)e FA(\035)k FB(is)c(su\016cien)n(tly)g(small,)h(w)n (e)f(can)g(ev)n(en)g(c)n(ho)r(ose)e FA(c)2732 3490 y Fz(N)2828 3478 y Fy(\030)h FA(N)3001 3447 y Fv(\000)p Fx(1)3123 3478 y FB([12)o(],)j(in)515 3577 y(that)28 b(case)e(one)i(has)f(the)h(stronger)d(result)1359 3830 y Fq(E)1414 3790 y Fx(+)p Fz(;")1414 3854 y(N)1534 3688 y Fw(")1613 3751 y(X)1582 3929 y Fz(x)p Fv(2)p Fx(\003)1710 3937 y Fu(N)1777 3830 y FA(\036)1826 3842 y Fz(x)1869 3688 y Fw(#)1940 3830 y Fy(\025)e FA(C)34 b FB(log)14 b FA(N)22 b Fy(j)p FB(\003)2412 3842 y Fz(N)2475 3830 y Fy(j)14 b FA(:)515 4095 y Fo(Thir)l(d)35 b(statement.)50 b FB(Since)32 b FA(\025)f FB(=)f(0)i(in)g(all)g(the)g(pro)r(of,)h(w)n (e)f(omit)g(it)h(from)e(the)i(notations.)515 4194 y(Our)g(pro)r(of)g (is)h(based)f(on)h(the)g(follo)n(wing)f(estimate:)49 b(There)34 b(exist)f FA(\021)2737 4206 y Fx(0)2809 4194 y FB(and)g FA(c)h(>)f FB(0)g(suc)n(h)515 4294 y(that,)28 b(for)f(all)g FA(B)g Fy(\032)c FB(\003)k(and)h(all)f FA(\035)f(>)c(\035)1703 4306 y Fx(0)1741 4294 y FB(,)1335 4477 y FA(\027)1376 4489 y Fz(N)s(;)p Fx(+)p Fz(;\035)1565 4477 y FB(\()p Fy(A)d(\\)g FA(B)27 b FB(=)c Fy(;)p FB(\))f Fy(\024)h FA(e)2157 4442 y Fv(\000)p Fz(c)p Fv(j)10 b Fx(log)i Fz(\035)r Fv(jj)p Fz(B)s Fv(j)2535 4477 y FA(:)650 b FB(\(2.6\))515 4659 y(Let)28 b(us)f(\014rst)h(assume)f(that)h (\(2.6\))f(holds)h(and)f(pro)n(v)n(e)f(the)j(t)n(w)n(o)e(statemen)n(ts) g(of)h(the)g(Theo-)515 4759 y(rem.)36 b(The)28 b(\014rst)f(statemen)n (t)g(is)g(v)n(ery)g(easy:)35 b(By)27 b(the)h(usual)f(decomp)r(osition)g (o)n(v)n(er)f(pinned)p Black Black eop end %%Page: 13 13 TeXDict begin 13 12 bop Black 515 232 a Fr(En)n(tropic)22 b(repulsion)g(in)f(external)h(\014eld;)g(v)n(ersion)f(from)g(July)g(3,) f(2003)1118 b FB(13)p Black 515 523 a(sites,)27 b(and)h(FK)n(G)f (inequalities,)791 718 y(E)848 730 y Fz(N)s(;)p Fx(+)p Fz(;)p Fx(0)p Fz(;\035)1089 718 y FB(\()p FA(X)1190 730 y Fz(i)1218 718 y FB(\))c(=)1368 639 y Fw(X)1361 817 y Fz(R)p Fv(\025)p Fx(1)1597 639 y Fw(X)1557 817 y Fz(A)p Fv(\032)p Fx(\003)1704 825 y Fu(N)1510 877 y Fz(d)p Fx(\()p Fz(A;x)p Fx(\)=)p Fz(R)1819 718 y FA(\027)1860 730 y Fz(N)s(;)p Fx(+)p Fz(;\035)2048 718 y FB(\()p FA(A)p FB(\))14 b(E)2245 730 y Fz(A)2295 714 y Fm(c)2325 730 y Fz(;)p Fx(+)p Fz(;)p Fx(0)p Fz(;)p Fx(0)2506 718 y FB(\()p FA(X)2607 730 y Fz(i)2634 718 y FB(\))1273 1021 y Fy(\024)1368 942 y Fw(X)1361 1120 y Fz(R)p Fv(\025)p Fx(1)1597 942 y Fw(X)1557 1120 y Fz(A)p Fv(\032)p Fx(\003)1704 1128 y Fu(N)1510 1180 y Fz(d)p Fx(\()p Fz(A;x)p Fx(\)=)p Fz(R)1819 1021 y FA(\027)1860 1033 y Fz(N)s(;)p Fx(+)p Fz(;\035)2048 1021 y FB(\()p FA(A)p FB(\))90 b(sup)2203 1094 y Fv(j)p Fz(j)s Fv(\000)p Fz(i)p Fv(j)p Fx(=)p Fz(R)2464 1021 y FB(E)2521 1036 y Fs(Z)2560 1019 y Fm(2)2591 1036 y Fv(nf)p Fz(j)s Fv(g)p Fz(;)p Fx(+)p Fz(;)p Fx(0)p Fz(;)p Fx(0)2905 1021 y FB(\()p FA(X)3006 1033 y Fz(i)3033 1021 y FB(\))14 b FA(:)515 1357 y FB(Since)29 b(E)790 1372 y Fs(Z)829 1355 y Fm(2)860 1372 y Fv(nf)p Fz(j)s Fv(g)p Fz(;)p Fx(+)p Fz(;)p Fx(0)p Fz(;)p Fx(0)1174 1357 y FB(\()p FA(X)1275 1369 y Fz(i)1302 1357 y FB(\))d Fy(\024)f FA(C)20 b FB(log)14 b FA(R)29 b FB(uniformly)g(in)g FA(j)34 b FB(suc)n(h)29 b(that)g Fy(j)p FA(j)24 b Fy(\000)19 b FA(i)p Fy(j)25 b FB(=)g FA(R)k FB([20)o(],)h(the)515 1456 y(\014rst)d(b)r(ound)h(is)g(pro)n(v)n(ed.)639 1556 y(Let)19 b(us)f(no)n(w)g(establish)h(the)g(p)r(ositivit)n(y)f(of)g(the) h(mass.)34 b(Decomp)r(osing)17 b(again)h(according)515 1655 y(to)27 b(the)h(pinned)g(sites,)g(w)n(e)f(get)895 1850 y(E)952 1862 y Fz(N)s(;)p Fx(+)p Fz(;)p Fx(0)p Fz(;\035)1193 1850 y FB(\()p FA(X)1294 1862 y Fz(i)1322 1850 y FA(X)1391 1862 y Fz(j)1426 1850 y FB(\))c(=)1609 1771 y Fw(X)1569 1949 y Fz(A)p Fv(\032)p Fx(\003)1716 1957 y Fu(N)1606 2043 y Fz(i)p Fv(6)1629 2009 y Fu(A)1672 1992 y Fm(c)1632 2043 y Fv($)t Fz(j)1783 1850 y FA(\027)1824 1862 y Fz(N)s(;)p Fx(+)p Fz(;\035)2013 1850 y FB(\()p FA(A)p FB(\))14 b(E)2210 1862 y Fz(A)2260 1846 y Fm(c)2289 1862 y Fz(;)p Fx(+)p Fz(;)p Fx(0)p Fz(;)p Fx(0)2470 1850 y FB(\()p FA(X)2571 1862 y Fz(i)2599 1850 y FA(X)2668 1862 y Fz(j)2702 1850 y FB(\))g FA(;)1713 2183 y FB(+)1836 2104 y Fw(X)1796 2282 y Fz(A)p Fv(\032)p Fx(\003)1943 2290 y Fu(N)1833 2376 y Fz(i)1856 2342 y Fu(A)1899 2325 y Fm(c)1859 2376 y Fv($)t Fz(j)2010 2183 y FA(\027)2051 2195 y Fz(N)s(;)p Fx(+)p Fz(;\035)2240 2183 y FB(\()p FA(A)p FB(\))g(E)2437 2195 y Fz(A)2487 2179 y Fm(c)2516 2195 y Fz(;)p Fx(+)p Fz(;)p Fx(0)p Fz(;)p Fx(0)2697 2183 y FB(\()p FA(X)2798 2195 y Fz(i)2826 2183 y FA(X)2895 2195 y Fz(j)2929 2183 y FB(\))g FA(;)515 2585 y FB(where)29 b FA(i)813 2538 y Fz(A)863 2513 y Fm(c)812 2585 y Fy($)d FA(j)35 b FB(means)29 b(that)g FA(i)h FB(and)f FA(j)35 b FB(are)28 b(connected)i(b)n(y)f(a)g (path)h(con)n(taining)e(only)h(sites)515 2708 y(of)e(\003)667 2720 y Fz(N)748 2708 y Fy(n)18 b FA(A)p FB(,)28 b(and)g FA(i)22 b Fy(6)1136 2661 y Fz(A)1186 2636 y Fm(c)1134 2708 y Fy($)i FA(j)32 b FB(is)c(the)g(complemen)n(tary)e(ev)n(en)n(t.) 639 2835 y(Supp)r(ose)31 b FA(i)c Fy(6)1026 2788 y Fz(A)1076 2763 y Fm(c)1024 2835 y Fy($)g FA(j)36 b FB(o)r(ccurs.)44 b(Let)30 b FA(\015)1695 2847 y Fz(i)1753 2835 y FB(b)r(e)h(the)f (innermost)g(closed)g(path)g(of)g(pinned)h(sites)515 2935 y(surrounding)18 b FA(j)24 b FB(\(p)r(ossibly)c(using)f(sites)g (outside)h(from)f(\003)2282 2947 y Fz(N)2344 2935 y FB(\),)j(and)d(let) h FA(\015)2729 2947 y Fz(j)2784 2935 y FB(b)r(e)f(the)h(analogous)515 3034 y(ob)5 b(ject)31 b(for)g FA(j)5 b FB(.)49 b(If)32 b FA(\015)1142 3046 y Fz(i)1201 3034 y FB(do)r(es)f(not)h(surround)e FA(j)5 b FB(,)33 b(then)f(let)g FA(\015)i FB(=)c FA(\015)2526 3046 y Fz(i)2553 3034 y FB(,)j(otherwise)e(let)g FA(\015)k FB(=)29 b FA(\015)3321 3046 y Fz(j)3356 3034 y FB(.)515 3165 y(Observ)n(e)k(that)i(under)f FA(i)h Fy(6)1336 3118 y Fz(A)1386 3093 y Fm(c)1334 3165 y Fy($)f FA(j)5 b FB(,)37 b FA(\015)i FB(surrounds)33 b(only)i(one)f(of)h(the)g(t)n(w)n(o)e (sites,)k(and)d(is)h(the)515 3264 y(innermost)29 b(path)h(with)g(this)h (prop)r(ert)n(y)-7 b(.)42 b(Supp)r(ose,)31 b(for)e(de\014niteness)h (that)g(it)g(surrounds)515 3364 y FA(i)p FB(.)59 b(W)-7 b(e)36 b(then)g(b)r(ound)g(the)f(\014rst)g(term)h(as)e(follo)n(ws,)i (writing)f(in)n(t\()p FA(\015)5 b FB(\))36 b(for)f(the)g(set)h(of)f (site)515 3464 y(surrounded)26 b(b)n(y)i FA(\015)k FB(or)26 b(along)h FA(\015)5 b FB(,)872 3646 y(E)929 3658 y Fz(N)s(;)p Fx(+)p Fz(;)p Fx(0)p Fz(;\035)1170 3646 y FB(\()p FA(X)1271 3658 y Fz(i)1299 3646 y FA(X)1368 3658 y Fz(j)1417 3646 y Fy(j)14 b FA(\015)5 b FB(\))22 b Fy(\024)h FB(E)1701 3661 y Fx(\003)1746 3669 y Fu(N)1799 3661 y Fv(n)p Fx(in)n(t\()p Fz(\015)t Fx(\))p Fz(;)p Fx(+)p Fz(;)p Fx(0)p Fz(;\035)2190 3646 y FB(\()p FA(X)2291 3658 y Fz(j)2326 3646 y FB(\))g(E)2438 3661 y Fx(in)n(t)o(\()p Fz(\015)t Fx(\))p Fv(n)p Fz(\015)t(;)p Fx(+)p Fz(;)p Fx(0)p Fz(;)p Fx(0)2860 3646 y FB(\()p FA(X)2961 3658 y Fz(i)2989 3646 y FB(\))1556 3771 y Fy(\024)g FB(E)1701 3783 y Fx(\003)1746 3791 y Fu(N)1799 3783 y Fz(;)p Fx(+)p Fz(;)p Fx(0)p Fz(;\035)1986 3771 y FB(\()p FA(X)2087 3783 y Fz(j)2122 3771 y FB(\))g(E)2234 3786 y Fx(in)n(t)o(\()p Fz(\015)t Fx(\))p Fv(n)p Fz(\015)t(;)p Fx(+)p Fz(;)p Fx(0)p Fz(;)p Fx(0)2656 3771 y FB(\()p FA(X)2757 3783 y Fz(i)2785 3771 y FB(\))14 b FA(:)515 3990 y FB(Since)30 b(a)n(v)n(eraging)d(the)k(last)e(exp)r(ectation)h(o) n(v)n(er)f FA(\015)35 b FB(yields)30 b(E)2415 4002 y Fz(N)s(;)p Fx(+)p Fz(;)p Fx(0)p Fz(;\035)2656 3990 y FB(\()p FA(X)2757 4002 y Fz(i)2784 3990 y FA(;)e(i)f Fy(6)2893 3943 y Fz(A)2943 3918 y Fm(c)2891 3990 y Fy($)g FA(j;)h(\015)k FB(=)27 b FA(\015)3296 4002 y Fz(i)3324 3990 y FB(\),)515 4090 y(w)n(e)g(see)g(that)796 4194 y Fw(X)756 4372 y Fz(A)p Fv(\032)p Fx(\003)903 4380 y Fu(N)793 4465 y Fz(i)p Fv(6)816 4432 y Fu(A)859 4415 y Fm(c)819 4465 y Fv($)t Fz(j)970 4273 y FA(\027)1011 4285 y Fz(N)s(;)p Fx(+)p Fz(;\035)1200 4273 y FB(\()p FA(A)p FB(\))14 b(E)1397 4285 y Fz(A)1447 4268 y Fm(c)1477 4285 y Fz(;)p Fx(+)p Fz(;)p Fx(0)p Fz(;)p Fx(0)1657 4273 y FB(\()p FA(X)1758 4285 y Fz(i)1786 4273 y FA(X)1855 4285 y Fz(j)1890 4273 y FB(\))k Fy(\000)g FB(E)2080 4285 y Fz(N)s(;)p Fx(+)p Fz(;)p Fx(0)p Fz(;\035)2321 4273 y FB(\()p FA(X)2422 4285 y Fz(i)2450 4273 y FB(\)E)2539 4285 y Fz(N)s(;)p Fx(+)p Fz(;)p Fx(0)p Fz(;\035)2780 4273 y FB(\()p FA(X)2881 4285 y Fz(j)2916 4273 y FB(\))24 b Fy(\024)e FB(0)14 b FA(:)515 4634 y FB(Therefore,)26 b(it)i(only)f(remains)g(to)h(pro)n(v)n(e)d(that)1400 4750 y Fw(X)1359 4928 y Fz(A)p Fv(\032)p Fx(\003)1506 4936 y Fu(N)1396 5022 y Fz(i)1419 4988 y Fu(A)1462 4971 y Fm(c)1422 5022 y Fv($)t Fz(j)1574 4829 y FA(\027)1615 4841 y Fz(N)s(;)p Fx(+)p Fz(;\035)1803 4829 y FB(\()p FA(A)p FB(\))f(E)2010 4841 y Fz(A)2060 4825 y Fm(c)2089 4841 y Fz(;)p Fx(+)p Fz(;)p Fx(0)p Fz(;)p Fx(0)2270 4829 y FB(\()p FA(X)2371 4841 y Fz(i)2398 4829 y FA(X)2467 4841 y Fz(j)2502 4829 y FB(\))p Black Black eop end %%Page: 14 14 TeXDict begin 14 13 bop Black 515 232 a Fr(En)n(tropic)22 b(repulsion)g(in)f(external)h(\014eld;)g(v)n(ersion)f(from)g(July)g(3,) f(2003)1118 b FB(14)p Black 515 523 a(is)24 b(exp)r(onen)n(tially)h (small)f(in)h Fy(j)p FA(i)13 b Fy(\000)g FA(j)5 b Fy(j)p FB(.)36 b(This)25 b(follo)n(ws)e(from)i(\(2.6\).)36 b(Indeed,)25 b(this)h(expression)515 623 y(is)h(b)r(ounded)h(ab)r(o)n(v)n(e)e(b)n(y) 1038 726 y Fw(X)921 904 y Fz(R)971 912 y Fm(1)1003 904 y Fv(\025)p Fx(0)p Fz(;R)1158 912 y Fm(2)1190 904 y Fv(\025)p Fx(0)1565 726 y Fw(X)1446 941 y Fz(A)p Fv(\032)p Fx(\003)1593 949 y Fu(N)1647 941 y Fz(;)11 b(i)1701 907 y Fu(A)1744 890 y Fm(c)1704 941 y Fv($)t Fz(j)1289 1004 y(d)p Fx(\()p Fz(A;x)p Fx(\)=)p Fz(R)1585 1012 y Fm(1)1616 1004 y Fz(;d)p Fx(\()p Fz(A;y)r Fx(\)=)p Fz(R)1930 1012 y Fm(2)1975 805 y FA(\027)2016 817 y Fz(N)s(;)p Fx(+)p Fz(;\035)2205 805 y FB(\()p FA(A)p FB(\))24 b(E)2412 817 y Fz(A)2462 800 y Fm(c)2491 817 y Fz(;)p Fx(+)p Fz(;)p Fx(0)p Fz(;)p Fx(0)2671 805 y FB(\()p FA(X)2772 817 y Fz(i)2800 805 y FA(X)2869 817 y Fz(j)2904 805 y FB(\))14 b FA(:)515 1164 y FB(No)n(w,)27 b(pro)r(ceeding)g(as)f(ab)r(o)n(v)n(e,)664 1377 y(E)721 1389 y Fz(A)771 1373 y Fm(c)800 1389 y Fz(;)p Fx(+)p Fz(;)p Fx(0)p Fz(;)p Fx(0)980 1377 y FB(\()p FA(X)1081 1389 y Fz(i)1109 1377 y FA(X)1178 1389 y Fz(j)1213 1377 y FB(\))d Fy(\024)1356 1285 y Fw(\020)1405 1377 y FB(E)1462 1389 y Fz(A)1512 1373 y Fm(c)1541 1389 y Fz(;)p Fx(+)p Fz(;)p Fx(0)p Fz(;)p Fx(0)1722 1377 y FB(\()p FA(X)1830 1343 y Fx(2)1823 1397 y Fz(i)1867 1377 y FB(\)E)1956 1389 y Fz(A)2006 1373 y Fm(c)2035 1389 y Fz(;)p Fx(+)p Fz(;)p Fx(0)p Fz(;)p Fx(0)2215 1377 y FB(\()p FA(X)2323 1343 y Fx(2)2316 1397 y Fz(j)2360 1377 y FB(\))2392 1285 y Fw(\021)2442 1302 y Fx(1)p Fz(=)p Fx(2)2570 1377 y Fy(\024)f FA(C)e FB(log)14 b FA(R)2920 1389 y Fx(1)2971 1377 y FB(log)h FA(R)3156 1389 y Fx(2)3207 1377 y FA(:)515 1572 y FB(Moreo)n(v)n(er,)25 b(it)j(follo)n(ws)e(from)i(\(2.6\))f(that) 1037 1679 y Fw(X)917 1895 y Fz(A)p Fv(\032)p Fx(\003)1064 1903 y Fu(N)1118 1895 y Fz(;)11 b(i)1172 1861 y Fu(A)1215 1844 y Fm(c)1175 1895 y Fv($)t Fz(j)761 1958 y(d)p Fx(\()p Fz(A;x)p Fx(\)=)p Fz(R)1057 1966 y Fm(1)1088 1958 y Fz(;d)p Fx(\()p Fz(A;y)r Fx(\)=)p Fz(R)1402 1966 y Fm(2)1447 1758 y FA(\027)1488 1770 y Fz(N)s(;)p Fx(+)p Fz(;\035)1676 1758 y FB(\()p FA(A)p FB(\))24 b Fy(\024)f FA(e)1953 1724 y Fv(\000)p Fz(C)t Fv(j)10 b Fx(log)i Fz(\035)r Fv(j)19 b(j)p Fz(i)p Fv(\000)p Fz(j)s Fv(j)2412 1758 y FA(e)2451 1724 y Fv(\000)p Fz(C)t Fv(j)10 b Fx(log)i Fz(\035)r Fv(j)19 b Fx(\()p Fz(R)2836 1732 y Fm(1)2868 1699 y(2)2900 1724 y Fx(+)p Fz(R)3001 1732 y Fm(2)3034 1699 y(2)3066 1724 y Fx(\))3110 1758 y FA(;)515 2117 y FB(pro)n(vided)26 b FA(\035)31 b FB(is)c(c)n(hosen)g(large)f(enough.) 36 b(The)28 b(statemen)n(t)g(follo)n(ws.)639 2262 y(Let)36 b(us)f(turn)h(no)n(w)f(to)g(the)h(pro)r(of)f(of)42 b(\(2.6\).)60 b(The)36 b(con)n(trol)e(of)i(the)g(distribution)f(of)515 2361 y(pinned)d(sites)f(is)g(done)g(similarly)f(as)h(in)g([17)o(,)h(23) o(,)f(8].)48 b(Let)31 b FA(B)i Fy(\032)c FB(\003)2652 2373 y Fz(N)2715 2361 y FB(.)48 b(W)-7 b(e)31 b(set)h FA(B)3129 2373 y Fx(0)3195 2361 y FB(=)d FA(B)t FB(,)515 2461 y(and)e(de\014ne)1246 2560 y FA(B)1309 2572 y Fz(k)q Fx(+1)1457 2560 y FB(=)c FA(B)1608 2572 y Fz(k)1667 2560 y Fy([)c(f)p FA(x)k Fy(2)g Fq(Z)1986 2526 y Fx(2)2061 2560 y FB(:)37 b FA(d)p FB(\()p FA(x;)14 b(B)2343 2572 y Fz(k)2385 2560 y FB(\))23 b(=)f(1)p Fy(g)14 b FA(:)515 2702 y FB(W)-7 b(e)28 b(then)g(ha)n(v)n(e)840 2872 y FA(\027)881 2884 y Fz(N)s(;)p Fx(+)p Fz(;\035)1070 2872 y FB(\()p Fy(A)19 b(\\)g FA(B)27 b FB(=)22 b Fy(;)p FB(\))h Fy(\024)1624 2793 y Fw(X)1623 2972 y Fz(k)q Fv(\025)p Fx(0)1759 2872 y FA(\027)1800 2884 y Fz(N)s(;)p Fx(+)p Fz(;\035)1988 2872 y FB(\()p Fy(A)c(\\)g FA(B)2242 2884 y Fz(k)2306 2872 y FB(=)k Fy(;)14 b(j)2514 2851 y FB(\026)2487 2872 y Fy(A)k(\\)g FA(B)2707 2884 y Fz(k)q Fx(+1)2855 2872 y Fy(6)p FB(=)23 b Fy(;)p FB(\))14 b FA(;)515 3138 y FB(where)783 3117 y(\026)755 3138 y Fy(A)23 b FB(=)g FA(A)c Fy([)f FB(\(\003)1176 3150 y Fz(N)1239 3138 y FB(\))1271 3108 y Fx(c)1305 3138 y FB(.)37 b(It)28 b(is)g(therefore)e (enough)h(to)h(pro)n(v)n(e)e(that)1036 3308 y FA(\027)1077 3320 y Fz(N)s(;)p Fx(+)p Fz(;\035)1266 3308 y FB(\()p Fy(A)19 b(\\)g FA(B)1520 3320 y Fz(k)1584 3308 y FB(=)k Fy(;)14 b(j)1792 3287 y FB(\026)1765 3308 y Fy(A)j(\\)i FA(B)1985 3320 y Fz(k)q Fx(+1)2133 3308 y Fy(6)p FB(=)k Fy(;)p FB(\))g Fy(\024)f FA(e)2444 3274 y Fv(\000)p Fz(c)p Fv(j)11 b Fx(log)h Fz(\035)r Fv(j)f(j)p Fz(B)s Fv(j)2834 3308 y FA(:)515 3478 y FB(W)-7 b(e)28 b(then)g(write,)f(as)g(in)h([17)o (,)g(23)o(,)g(8)o(],)572 3789 y FA(\027)613 3801 y Fz(N)s(;)p Fx(+)p Fz(;\035)802 3789 y FB(\()p Fy(A)19 b(\\)g FA(B)1056 3801 y Fz(k)1120 3789 y FB(=)j Fy(;)14 b(j)1328 3768 y FB(\026)1300 3789 y Fy(A)k(\\)h FA(B)1521 3801 y Fz(k)q Fx(+1)1669 3789 y Fy(6)p FB(=)k Fy(;)p FB(\))f Fy(\024)1941 3594 y Fw(8)1941 3669 y(>)1941 3694 y(<)1941 3843 y(>)1941 3868 y(:)2050 3710 y(X)2015 3889 y Fz(C)t Fv(\032)p Fz(B)2169 3898 y Fu(k)2219 3789 y FA(\035)2267 3755 y Fv(j)p Fz(C)t Fv(j)2494 3789 y FB(inf)2411 3847 y Fz(A)p Fv(\\)p Fz(B)2556 3856 y Fu(k)2592 3847 y Fx(=)p Fv(;)2393 3897 y Fx(\026)2376 3912 y Fz(A)p Fv(\\)p Fz(B)2521 3921 y Fu(k)q Fm(+1)2628 3912 y Fv(6)p Fx(=)p Fv(;)2737 3727 y FA(Z)2794 3742 y Fx(\()p Fz(A)p Fv([)p Fz(C)t Fx(\))2993 3726 y Fm(c)3021 3742 y Fz(;)p Fx(+)p Fz(;)p Fx(0)p 2737 3770 413 4 v 2811 3846 a FA(Z)2868 3858 y Fz(A)2918 3842 y Fm(c)2947 3858 y Fz(;)p Fx(+)p Fz(;)p Fx(0)3159 3594 y Fw(9)3159 3669 y(>)3159 3694 y(=)3159 3843 y(>)3159 3868 y(;)3232 3615 y Fv(\000)p Fx(1)1853 4188 y Fy(\024)1941 3993 y Fw(8)1941 4068 y(>)1941 4093 y(<)1941 4242 y(>)1941 4267 y(:)2015 4188 y FA(\035)2063 4154 y Fv(j)p Fz(B)2133 4163 y Fu(k)2169 4154 y Fv(j)2325 4188 y FB(inf)2242 4246 y Fz(A)p Fv(\\)p Fz(B)2387 4255 y Fu(k)2423 4246 y Fx(=)p Fv(;)2224 4296 y Fx(\026)2207 4311 y Fz(A)p Fv(\\)p Fz(B)2352 4320 y Fu(k)q Fm(+1)2459 4311 y Fv(6)p Fx(=)p Fv(;)2567 4126 y FA(Z)2624 4141 y Fx(\()p Fz(A)p Fv([)p Fz(B)2795 4150 y Fu(k)2831 4141 y Fx(\))2857 4125 y Fm(c)2887 4141 y Fz(;)p Fx(+)p Fz(;)p Fx(0)p 2567 4169 447 4 v 2659 4245 a FA(Z)2716 4257 y Fz(A)2766 4241 y Fm(c)2795 4257 y Fz(;)p Fx(+)p Fz(;)p Fx(0)3024 3993 y Fw(9)3024 4068 y(>)3024 4093 y(=)3024 4242 y(>)3024 4267 y(;)3098 4014 y Fv(\000)p Fx(1)3215 4188 y FA(:)515 4483 y FB(Let)e(us)g(n)n(um)n(b)r(er)f(the)h(sites)g(of)g FA(B)1512 4495 y Fz(k)1576 4483 y FB(=)i Fy(f)p FA(t)1735 4495 y Fx(1)1772 4483 y FA(;)14 b(:)g(:)g(:)g(;)g(t)1987 4498 y Fv(j)p Fz(B)2057 4507 y Fu(k)2093 4498 y Fv(j)2117 4483 y Fy(g)19 b FB(in)h(suc)n(h)g(a)f(w)n(a)n(y)g(that)h FA(t)2871 4495 y Fx(1)2928 4483 y FB(is)g(a)f(neigh)n(b)r(or)515 4582 y(of)26 b(a)g(site)g(of)942 4561 y(\026)920 4582 y FA(A)16 b Fy(\\)g FA(B)1132 4594 y Fz(k)q Fx(+1)1257 4582 y FB(,)26 b(and)g(eac)n(h)f FA(t)1681 4594 y Fz(k)1722 4582 y FB(,)i FA(k)f(>)c FB(1,)k(is)g(a)g(neigh)n(b)r(or)f(of)h(at)g (least)g(one)g FA(t)3076 4594 y Fz(j)3111 4582 y FB(,)g FA(j)i(<)23 b(k)s FB(.)515 4682 y(W)-7 b(e)28 b(write)f(the)h(last)f (fraction)g(as)g(a)g(telescoping)g(pro)r(duct:)1210 4878 y FA(Z)1267 4893 y Fx(\()p Fz(A)p Fv([)p Fz(B)1438 4902 y Fu(k)1474 4893 y Fx(\))1500 4876 y Fm(c)1529 4893 y Fz(;)p Fx(+)p Fz(;)p Fx(0)p 1210 4920 V 1302 4997 a FA(Z)1359 5009 y Fz(A)1409 4992 y Fm(c)1438 5009 y Fz(;)p Fx(+)p Fz(;)p Fx(0)1690 4940 y FB(=)1778 4829 y Fv(j)p Fz(B)1848 4838 y Fu(k)1884 4829 y Fv(j)1788 4861 y Fw(Y)1780 5039 y Fz(k)q Fx(=1)1964 4878 y FA(Z)2021 4893 y Fx(\()p Fz(A)p Fv([f)p Fz(t)2201 4901 y Fm(1)2233 4893 y Fz(;:::)o(;t)2357 4902 y Fu(k)2393 4893 y Fv(g)p Fx(\))2453 4876 y Fm(c)2482 4893 y Fz(;)p Fx(+)p Fz(;)p Fx(0)p 1927 4920 720 4 v 1927 4997 a FA(Z)1984 5012 y Fx(\()p Fz(A)p Fv([f)p Fz(t)2164 5020 y Fm(1)2196 5012 y Fz(;:::)o(;t)2320 5021 y Fu(k)q Fn(\000)p Fm(1)2429 5012 y Fv(g)p Fx(\))2489 4995 y Fm(c)2519 5012 y Fz(;)p Fx(+)p Fz(;)p Fx(0)2670 4940 y FA(:)p Black Black eop end %%Page: 15 15 TeXDict begin 15 14 bop Black 515 232 a Fr(En)n(tropic)22 b(repulsion)g(in)f(external)h(\014eld;)g(v)n(ersion)f(from)g(July)g(3,) f(2003)1118 b FB(15)p Black 515 523 a(The)27 b(conclusion)g(follo)n(ws) g(once)g(w)n(e)g(pro)n(v)n(e)f(that)i(there)f(exists)g FA(c)c(>)g FB(0)k(suc)n(h)h(that)1628 687 y FA(Z)1685 702 y Fx(\()p Fz(C)t Fv([f)p Fz(i)p Fv(g)p Fx(\))1925 686 y Fm(c)1954 702 y Fz(;)p Fx(+)p Fz(;)p Fx(0)p 1628 730 454 4 v 1722 806 a FA(Z)1779 818 y Fz(C)1831 802 y Fm(c)1860 818 y Fz(;)p Fx(+)p Fz(;)p Fx(0)2115 749 y Fy(\025)23 b FA(c)14 b(;)515 979 y FB(uniformly)27 b(in)h FA(C)h Fy(\032)23 b FB(\003)1224 991 y Fz(N)1287 979 y FB(,)k(and)h FA(i)f FB(neigh)n(b)r(oring)f FA(C)6 b FB(.)535 1143 y FA(Z)592 1158 y Fx(\()p Fz(C)t Fv([f)p Fz(i)p Fv(g)p Fx(\))832 1141 y Fm(c)861 1158 y Fz(;)p Fx(+)p Fz(;)p Fx(0)p 535 1186 V 629 1262 a FA(Z)686 1274 y Fz(C)738 1258 y Fm(c)767 1274 y Fz(;)p Fx(+)p Fz(;)p Fx(0)1022 1205 y FB(=)28 b(lim)1109 1259 y Fz(\017)p Fv(&)p Fx(0)1260 1149 y FB(1)p 1260 1186 42 4 v 1264 1262 a FA(\017)1312 1205 y Fq(P)1363 1220 y Fx(\()p Fz(C)t Fv([f)p Fz(i)p Fv(g)p Fx(\))1603 1203 y Fm(c)1632 1220 y Fz(;)p Fx(+)p Fz(;)p Fx(0)1759 1205 y FB(\()p Fy(j)p FA(X)1883 1217 y Fz(i)1911 1205 y Fy(j)23 b(\024)g FA(\017)p FB(\))g Fy(\025)28 b FB(lim)2222 1259 y Fz(\017)p Fv(&)p Fx(0)2372 1149 y FB(1)p 2372 1186 V 2376 1262 a FA(\017)2424 1205 y Fq(P)2475 1220 y Fs(Z)2514 1203 y Fm(2)2546 1220 y Fz(;)p Fx(+)p Fz(;)p Fx(0)2673 1205 y FB(\()p Fy(j)p FA(X)2797 1217 y Fz(i)2825 1205 y Fy(j)23 b(\024)g FA(\017)14 b Fy(j)g FA(X)3113 1217 y Fz(j)3170 1205 y FB(=)23 b(0\))14 b FA(;)515 1435 y FB(where)37 b FA(j)43 b FB(in)38 b(the)g(last)g (probabilit)n(y)f(is)g(a)h(site)g(of)f FA(C)45 b FB(whic)n(h)37 b(is)h(nearest)f(neigh)n(b)r(or)g(to)g FA(i)515 1534 y FB(\(the)25 b(last)g(inequalit)n(y)f(follo)n(ws)g(from)g(FK)n(G\).)h (Let)g(us)f(estimate)h(this)g(probabilit)n(y)-7 b(.)35 b(By)25 b(the)515 1634 y(Mark)n(o)n(v)g(prop)r(ert)n(y)-7 b(,)27 b(w)n(e)g(ha)n(v)n(e)f(\()p FA(u)d Fy(\030)g FA(v)31 b FB(meaning)c FA(u)g FB(and)g FA(v)k FB(nearest)c(neigh)n(b)r(ors\)) 593 1816 y Fq(P)644 1831 y Fs(Z)683 1815 y Fm(2)715 1831 y Fz(;)p Fx(+)p Fz(;)p Fx(0)843 1816 y FB(\()p Fy(j)p FA(X)967 1828 y Fz(i)994 1816 y Fy(j)c(\024)g FA(\017)14 b Fy(j)g FA(X)1282 1828 y Fz(j)1339 1816 y FB(=)23 b(0\))1185 1993 y Fy(\025)1273 1880 y Fw(Z)1369 1993 y Fq(P)1420 2008 y Fs(Z)1459 1991 y Fm(2)1491 2008 y Fz(;)p Fx(+)p Fz(;)p Fx(0)1619 1993 y FB(\(d)p FA(X)d Fy(j)14 b FA(X)1892 2005 y Fz(j)1950 1993 y FB(=)23 b(0\))g(1)2177 2008 y Fv(f)p Fx(max)2333 2017 y Fu(k)q Fn(\030)p Fu(i)2447 2008 y Fz(X)2501 2017 y Fu(k)2538 2008 y Fz()34 b(\014)1027 2833 y Fz(c)1061 2821 y FB(.)57 b(W)-7 b(e)35 b(denote)g(b)n(y)f FA(h)1736 2833 y Fz(w)1789 2821 y FB(\()p FA(\014)t FB(\))i Fy(\025)e FB(0)g(the)h(v)-5 b(alue)34 b(of)h(the)g(b)r(oundary)e (\014eld)i(at)515 2921 y(whic)n(h)c(w)n(etting)g(tak)n(es)f(place)g (when)i FA(\025)d FB(=)f(0.)47 b(Since)31 b FA(\014)i(>)c(\014)2432 2933 y Fz(c)2497 2921 y FB(and)i FA(h)d Fy(\025)h FA(h)2880 2933 y Fz(w)2933 2921 y FB(\()p FA(\014)t FB(\))j(are)e(k)n(ept)515 3021 y(\014xed,)d(w)n(e)h(often)g(ligh)n(ten)f(the)h(notations)f(b)n(y) g(omitting)h(the)g(corresp)r(onding)d(subscripts.)639 3120 y(F)-7 b(or)27 b FA(N)37 b FB(ev)n(en,)27 b(consider)f(the)i (square)f(b)r(o)n(x)1116 3303 y(\003)1174 3315 y Fz(N)1259 3303 y FB(=)c Fy(f\000)p FA(N)r(=)p FB(2)16 b(+)i(1)p FA(;)c(:)g(:)g(:)g(;)g(N)r(=)p FB(2)p Fy(g)i(\002)i(f)p FB(0)p FA(;)c(:)g(:)g(:)f(;)h(N)27 b Fy(\000)18 b FB(1)p Fy(g)p FA(:)639 3485 y FB(In)27 b(the)h(complete)e(w)n(etting)h(regime) f FA(h)d Fy(\025)g FA(h)2005 3497 y Fz(w)2058 3485 y FB(\()p FA(\014)t FB(\),)28 b(when)f FA(\025)d FB(=)f(0)j(the)h(w)n (all)g(free)f(energy)515 3585 y(is)i(giv)n(en)g(b)n(y)g(the)h(surface)f (tension)g(in)h(the)g(horizon)n(tal)e(direction.)39 b(In)29 b(the)g(presence)f(of)g(a)515 3685 y(bulk)c(\014eld)g FA(\025)f(>)g FB(0,)h(the)h(latter)e(do)r(es)h(not)f(mak)n(e)g(sense)h (an)n(ymore)e(since)i(the)g Fy(\000)f FB(phase)h(isn't)515 3784 y(stable,)29 b(ho)n(w)n(ev)n(er)d(the)j(former)f(remains)g (meaningful)h(since)f(in)h(the)g(vicinit)n(y)g(of)g(the)g(w)n(all)515 3884 y(the)h Fy(\000)g FB(phase)g(is)g(stabilized)g(b)n(y)g(the)h(b)r (oundary)e(conditions.)44 b(W)-7 b(e)31 b(therefore)e(de\014ne)i(the) 515 3983 y(\(\014nite-v)n(olume\))c(w)n(all)g(free)h(energy)e(b)n(y)i (the)f(usual)h(form)n(ula,)1247 4208 y FA(\034)1283 4220 y Fx(b)r(d)1362 4208 y FB(\()p FA(\014)t(;)14 b(h;)g(\025;)g(N)9 b FB(\))24 b(=)f Fy(\000)1963 4152 y FB(1)p 1947 4189 76 4 v 1947 4265 a FA(N)2060 4208 y FB(log)2191 4152 y FA(Z)2248 4164 y Fv(\006)p Fz(;\014)s(;\025;h;)p Fx(\003)2544 4172 y Fu(N)p 2191 4189 410 4 v 2191 4265 a FA(Z)2248 4277 y Fx(+)p Fz(;\014)s(;\025;h;)p Fx(\003)2543 4285 y Fu(N)2624 4208 y FA(:)515 4438 y FB(The)j(next)h(lemma)g(states)f (that)g(the)h(e\013ect)g(of)g(the)g(bulk)g(\014eld)f FA(\025)h FB(on)g(the)g(surface)e(tension)515 4537 y(is)i(to)h (increase)e(the)i(latter)f(b)n(y)h(an)f(amoun)n(t)g(of)h(order)e(at)h (most)h FA(\025)2581 4507 y Fx(2)p Fz(=)p Fx(3+)p Fz(o)p Fx(\(1\))2854 4537 y FB(.)p Black 515 4703 a Fp(Lemma)j(3)p Black 42 w Fj(F)-7 b(or)25 b(all)g FA(\014)i(>)c(\014)1412 4715 y Fz(c)1471 4703 y Fj(and)j FA(h)d(>)f(h)1837 4715 y Fz(w)1891 4703 y FB(\()p FA(\014)t FB(\))p Fj(,)27 b(there)e(exist)h FA(C)j(>)23 b FB(0)p Fj(,)i FA(\025)2775 4715 y Fx(0)2836 4703 y FA(>)e FB(0)i Fj(and)g FA(K)k(>)22 b FB(0)515 4803 y Fj(suc)n(h)27 b(that,)h(for)f(all)g FB(0)c FA(<)g(\025)g(<)g(\025)1507 4815 y Fx(0)1572 4803 y Fj(and)k FA(N)32 b(>)23 b(K)6 b(\025)2045 4773 y Fv(\000)p Fx(2)p Fz(=)p Fx(3)2201 4803 y Fy(j)14 b FB(log)g FA(\025)p Fy(j)2430 4773 y Fx(3)2468 4803 y Fj(,)760 4985 y FA(\034)796 4997 y Fx(b)r(d)876 4985 y FB(\()p FA(\014)t(;)g(h;)g FB(0)p FA(;)g(N)9 b FB(\))23 b Fy(\024)f FA(\034)1414 4997 y Fx(b)r(d)1494 4985 y FB(\()p FA(\014)t(;)14 b(h;)g(\025;)g(N)9 b FB(\))23 b Fy(\024)g FA(\034)2039 4997 y Fx(b)r(d)2119 4985 y FB(\()p FA(\014)t(;)14 b(h;)g FB(0)p FA(;)g(N)9 b FB(\))18 b(+)g FA(C)6 b(\025)2725 4951 y Fx(2)p Fz(=)p Fx(3)2830 4985 y Fy(j)14 b FB(log)g FA(\025)p Fy(j)3059 4951 y Fx(2)3110 4985 y FA(:)p Black Black eop end %%Page: 17 17 TeXDict begin 17 16 bop Black 515 232 a Fr(En)n(tropic)22 b(repulsion)g(in)f(external)h(\014eld;)g(v)n(ersion)f(from)g(July)g(3,) f(2003)1118 b FB(17)p Black 639 523 a Fp(Pro)s(of)32 b(of)g(Lemma)f(3.)639 623 y FB(Let)f FA(F)843 635 y Fz(\025)886 623 y FB(\()p FA(\033)s FB(\))d(=)e FA(e)1156 581 y Fz(\025)1218 537 y Fk(P)1288 600 y Fu(x)p Fn(2)p Fm(\003)1398 614 y Fu(N)1466 581 y Fz(\033)1504 589 y Fu(x)1546 623 y FB(.)42 b(The)29 b(statemen)n(t)g(of)g(the)h(lemma)f(can)f(b)r(e)i (rewritten)f(in)515 722 y(the)f(follo)n(wing)e(form,)748 913 y Fy(h)p FA(F)833 925 y Fz(\025)877 913 y Fy(i)909 925 y Fx(+)p Fz(;\014)s(;)p Fx(0)p Fz(;h;)p Fx(\003)1198 933 y Fu(N)1278 913 y Fy(\025)d(h)p FA(F)1451 925 y Fz(\025)1495 913 y Fy(i)1527 925 y Fv(\006)p Fz(;\014)s(;)p Fx(0)p Fz(;h;)p Fx(\003)1817 933 y Fu(N)1896 913 y Fy(\025)g FA(e)2023 878 y Fv(\000)p Fz(C)2123 886 y Fm(4)2166 878 y Fz(\025)2205 853 y Fm(2)p Fu(=)p Fm(3)2308 878 y Fv(j)11 b Fx(log)h Fz(\025)p Fv(j)2495 853 y Fm(2)2539 878 y Fz(N)2602 913 y Fy(h)p FA(F)2687 925 y Fz(\025)2731 913 y Fy(i)2763 925 y Fx(+)p Fz(;\014)s(;)p Fx(0)p Fz(;h;)p Fx(\003)3052 933 y Fu(N)3123 913 y FA(:)515 1088 y FB(Since)32 b(the)g(\014rst)f(inequalit)n(y)h(is)f(a)h(direct)f(consequence)g(of)h (FK)n(G)f(inequalities,)i(w)n(e)e(only)515 1187 y(ha)n(v)n(e)26 b(to)i(pro)n(v)n(e)e(the)i(second)f(one.)639 1287 y(Let)i Fy(H)d FB(=)f FA(\025)1023 1257 y Fv(\000)p Fx(1)p Fz(=)p Fx(3)1180 1287 y Fy(j)14 b FB(log)g FA(\025)p Fy(j)1409 1257 y Fx(2)1475 1287 y FB(and)29 b Fy(S)1688 1299 y Fv(H)1775 1287 y FB(=)24 b Fy(f)p FA(x)h Fy(2)h FB(\003)2117 1299 y Fz(N)2218 1287 y FB(:)40 b FA(x)2328 1299 y Fx(2)2390 1287 y Fy(\024)25 b(H)q(g)j FB(b)r(e)i(the)f(strip)g(of)f(width)515 1387 y Fy(H)g FB(along)f(the)h(b)r(ottom)g(w)n(all.)639 1486 y(According)f(to)g(the)h(discussion)f(in)h(App)r(endix)h(A,)1004 1673 y FA(Z)1061 1685 y Fv(\006)p Fz(;\014)s(;\025;h;)p Fx(\003)1357 1693 y Fu(N)1436 1673 y Fy(\025)1556 1594 y Fw(X)1524 1772 y Fz(\015)t Fv(\032S)1656 1780 y Fn(H)1723 1673 y FA(w)r FB(\()p FA(\015)5 b FB(\))14 b FA(Z)1967 1689 y Fx(+)p Fz(;\014)s(;\025;)p Fx(\003)2203 1672 y Fm(+)2249 1689 y Fx(\()p Fz(\015)t Fx(\))2358 1673 y FA(Z)2415 1689 y Fv(\000)p Fz(;\014)s(;\025;h;)p Fx(\003)2711 1672 y Fn(\000)2758 1689 y Fx(\()p Fz(\015)t Fx(\))2867 1673 y FA(:)515 1933 y FB(T)-7 b(o)28 b(simplify)i(somewhat)e(the)h (notations)f(w)n(e)g(omit,)i(in)f(the)g(rest)f(of)h(the)g(pro)r(of,)g (the)g(sub-)515 2033 y(scripts)e FA(\014)32 b FB(and)27 b FA(h)p FB(,)h(and)f(write)h(simply)f(\003)1815 2003 y Fx(+)1898 2033 y FB(and)g(\003)2117 2003 y Fv(\000)2173 2033 y FB(.)639 2133 y(Our)33 b(\014rst)f(task)h(is)g(to)g(remo)n(v)n (e)e(the)i FA(\025)p FB(-dep)r(endence)h(in)f(the)h(last)e(equation.)53 b(Indeed)515 2232 y(our)25 b(main)h(to)r(ol,)g(the)g(random-line)f (represen)n(tation)f(brie\015y)i(describ)r(ed)g(in)g(App)r(endix)h(A,) 515 2332 y(only)g(applies)g(in)h(the)g(absence)f(of)g(bulk)h(\014eld.) 794 2519 y FA(Z)851 2535 y Fx(+)p Fz(;\025;)p Fx(\003)1026 2518 y Fm(+)1091 2519 y FA(Z)1148 2535 y Fv(\000)p Fz(;\025;)p Fx(\003)1324 2518 y Fn(\000)1400 2519 y Fy(\025)22 b FA(Z)1544 2535 y Fx(+)p Fz(;\025;)p Fx(\003)1719 2518 y Fm(+)1784 2519 y FA(Z)1841 2535 y Fv(\000)p Fz(;)p Fv(\000)p Fz(\025;)p Fx(\003)2069 2518 y Fn(\000)2145 2519 y FA(e)2184 2485 y Fv(\000)p Fx(2)p Fz(\025)11 b Fv(j)p Fx(\003)2384 2460 y Fn(\000)2434 2485 y Fx(\()p Fz(\015)t Fx(\))p Fv(j)1400 2698 y Fy(\025)1497 2639 y FA(Z)1554 2654 y Fx(+)p Fz(;\025;)p Fx(\003)1729 2638 y Fm(+)1794 2639 y FA(Z)1851 2654 y Fv(\000)p Fz(;)p Fv(\000)p Fz(\025;)p Fx(\003)2079 2638 y Fn(\000)p 1497 2679 635 4 v 1530 2755 a FA(Z)1587 2771 y Fx(+)p Fz(;)p Fx(0)p Fz(;)p Fx(\003)1756 2754 y Fm(+)1820 2755 y FA(Z)1877 2771 y Fx(+)p Fz(;)p Fx(0)p Fz(;)p Fx(\003)2046 2754 y Fn(\000)2165 2698 y FA(Z)2222 2714 y Fx(+)p Fz(;)p Fx(0)p Fz(;)p Fx(\003)2391 2697 y Fm(+)2455 2698 y FA(Z)2512 2714 y Fx(+)p Fz(;)p Fx(0)p Fz(;)p Fx(\003)2681 2697 y Fn(\000)2757 2698 y FA(e)2796 2664 y Fv(\000)p Fx(2)p Fz(\025)h Fv(H)f Fz(N)3077 2698 y FA(:)515 2923 y FB(W)-7 b(riting)29 b FA(x)e Fy(\030)e FA(\015)34 b FB(if)c FA(x)g FB(is)f(one)g(the)h(sites)f(whose)g(v)-5 b(alue)29 b(is)g(completely)h (determined)f(b)n(y)g FA(\015)5 b FB(,)515 3023 y(w)n(e)27 b(can)g(estimate)h(the)g(ratio)952 3166 y FA(Z)1009 3181 y Fx(+)p Fz(;\025;)p Fx(\003)1184 3165 y Fm(+)1249 3166 y FA(Z)1306 3181 y Fv(\000)p Fz(;)p Fv(\000)p Fz(\025;)p Fx(\003)1534 3165 y Fn(\000)p 952 3206 V 985 3282 a FA(Z)1042 3298 y Fx(+)p Fz(;)p Fx(0)p Fz(;)p Fx(\003)1211 3281 y Fm(+)1275 3282 y FA(Z)1332 3298 y Fx(+)p Fz(;)p Fx(0)p Fz(;)p Fx(\003)1501 3281 y Fn(\000)1620 3225 y FB(=)1718 3169 y FA(\026)1768 3181 y Fx(+)p Fz(;\025;)p Fx(\003)1943 3189 y Fu(N)2000 3169 y FB(\()p FA(\033)2079 3181 y Fz(x)2145 3169 y FB(=)23 b(1)p FA(;)k Fy(8)p FA(x)c Fy(\030)g FA(\015)5 b FB(\))p 1718 3206 892 4 v 1721 3282 a FA(\026)1771 3294 y Fx(+)p Fz(;)p Fx(0)p Fz(;)p Fx(\003)1940 3302 y Fu(N)1997 3282 y FB(\()p FA(\033)2076 3294 y Fz(x)2142 3282 y FB(=)22 b(1)p FA(;)28 b Fy(8)p FA(x)23 b Fy(\030)g FA(\015)5 b FB(\))2652 3169 y FA(Z)2709 3181 y Fx(+)p Fz(;\025;)p Fx(\003)2884 3189 y Fu(N)p 2652 3206 290 4 v 2655 3282 a FA(Z)2712 3294 y Fx(+)p Fz(;)p Fx(0)p Fz(;)p Fx(\003)2881 3302 y Fu(N)1620 3455 y Fy(\025)1718 3399 y FA(Z)1775 3411 y Fx(+)p Fz(;\025;)p Fx(\003)1950 3419 y Fu(N)p 1718 3436 V 1721 3512 a FA(Z)1778 3524 y Fx(+)p Fz(;)p Fx(0)p Fz(;)p Fx(\003)1947 3532 y Fu(N)2031 3455 y FA(:)515 3682 y FB(Here,)32 b(the)g(iden)n(tit)n(y)g(follo)n(ws) f(from)g(the)h(+)p FA(=)p Fy(\000)f FB(symmetry)g(of)h(the)g(mo)r(del,) h(and)e(the)h(last)515 3782 y(inequalit)n(y)d(is)h(a)f(consequence)g (of)h(FK)n(G)g(inequalities.)43 b(Collecting)30 b(all)f(these)h (estimates)515 3881 y(together,)d(w)n(e)g(get,)g(see)g(\(A.12\),)1204 4073 y FA(Z)1261 4085 y Fv(\006)p Fz(;\025;)p Fx(\003)1437 4093 y Fu(N)1518 4073 y Fy(\025)22 b FA(e)1644 4039 y Fv(\000)p Fx(2)p Fz(\025)12 b Fv(H)f Fz(N)1925 4073 y FA(Z)1982 4085 y Fx(+)p Fz(;\025;)p Fx(\003)2157 4093 y Fu(N)2274 3994 y Fw(X)2242 4172 y Fz(\015)t Fv(\032S)2374 4180 y Fn(H)2440 4073 y FA(q)2477 4085 y Fz(N)2540 4073 y FB(\()p FA(\015)5 b FB(\))14 b FA(;)515 4333 y FB(whic)n(h)33 b(is)g(precisely)f(what)i(w)n(e)e(w)n(ere)h(after.)53 b(A)n(t)34 b(this)f(stage,)h(it)g(is)f(p)r(ossible)g(to)g(use)g(the)515 4433 y(to)r(ols)27 b(discussed)g(in)h(App)r(endix)g(A)g(in)g(order)e (to)i(con)n(trol)e(the)i(last)f(sum.)639 4532 y(Let)k FA(K)36 b FB(b)r(e)30 b(a)g(su\016cien)n(tly)h(large)e(in)n(teger.)44 b(W)-7 b(e)31 b(split)f(the)h(slab)f Fy(S)2728 4544 y Fv(H)2820 4532 y FB(in)n(to)g FA(M)39 b FB(disjoin)n(t)515 4632 y(rectangles,)27 b Fy(R)997 4644 y Fx(1)1035 4632 y FA(;)14 b(:)g(:)g(:)g(;)g Fy(R)1290 4644 y Fz(M)1363 4632 y FB(,)30 b(with)f(heigh)n(t)f Fy(H)i FB(and)e(basis)g(of)h (length)g([)p Fy(H)2770 4602 y Fx(2)2807 4632 y FA(=)p FB(\()p FA(K)19 b FB(log)14 b Fy(H)q FB(\)],)30 b(ex-)515 4732 y(cept)j(p)r(ossibly)h(for)e(the)i(righ)n(tmost)f(one)g(whic)n(h)g (ma)n(y)g(ha)n(v)n(e)f(a)h(shorter)g(basis.)53 b(W)-7 b(e)34 b(also)515 4831 y(in)n(tro)r(duce)27 b(the)h(dual)f(sites)h FA(a)1441 4843 y Fz(k)1482 4831 y FB(,)f FA(k)f FB(=)d(0)p FA(;)14 b(:)g(:)g(:)f(;)h(M)9 b FB(,)27 b(de\014ned)h(b)n(y)928 5006 y FA(a)972 5018 y Fz(k)1036 5006 y FB(=)22 b(\()p Fy(\000)p FB(\()p FA(N)28 b Fy(\000)18 b FB(1\))p FA(=)p FB(2)f(+)h FA(k)s FB([)p Fy(H)1828 4972 y Fx(2)1865 5006 y FA(=)p FB(\()p FA(K)h FB(log)14 b Fy(H)q FB(\)])19 b Fy(^)g FB(\()p FA(N)27 b Fy(\000)18 b FB(1\))p FA(=)p FB(2)p FA(;)c FB(1)p FA(=)p FB(2\))g FA(:)p Black Black eop end %%Page: 18 18 TeXDict begin 18 17 bop Black 515 232 a Fr(En)n(tropic)22 b(repulsion)g(in)f(external)h(\014eld;)g(v)n(ersion)f(from)g(July)g(3,) f(2003)1118 b FB(18)p Black Black 310 912 a currentpoint currentpoint translate 0.53383 0.53383 scale neg exch neg exch translate 310 912 a @beginspecial 0 @llx 0 @lly 733 @urx 107 @ury 7330 @rwi @setspecial %%BeginDocument: isinglayer.pstex %!PS-Adobe-2.0 EPSF-2.0 %%Title: isinglayer.pstex %%Creator: fig2dev Version 3.2 Patchlevel 3d %%CreationDate: Mon Jul 1 10:43:58 2002 %%For: velenik@eupalidos.cmi.univ-mrs.fr (Yvan VELENIK, CR probabilites) %%BoundingBox: 0 0 733 107 %%Magnification: 1.0000 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save newpath 0 107 moveto 0 0 lineto 733 0 lineto 733 107 lineto closepath clip newpath -63.0 321.5 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def $F2psBegin 10 setmiterlimit 0.06000 0.06000 sc % % Fig objects follow % % Polyline 7.500 slw n 1200 3600 m 13200 3600 l 13200 4800 l 1200 4800 l cp gs col0 s gr % Polyline n 3600 3600 m 3600 4800 l gs col0 s gr % Polyline n 6000 3600 m 6000 4800 l gs col0 s gr % Polyline n 8400 3600 m 8400 4800 l gs col0 s gr % Polyline n 10800 3600 m 10800 4800 l gs col0 s gr % Polyline 30.000 slw n 13200 4800 m 13050 4800 l 13050 4725 l 12900 4725 l 12900 4425 l 12825 4425 l 12825 4200 l 12450 4200 l 12450 3975 l 11775 3975 l 11775 4275 l 12000 4275 l 12000 4575 l 11775 4575 l 11775 4350 l 11625 4350 l 11625 4125 l 11325 4125 l 11325 4275 l 11475 4275 l 11475 4425 l 11175 4425 l 11175 4575 l 11250 4575 l 11250 4800 l 10800 4800 l 10650 4800 l 10650 4725 l 10500 4725 l 10500 4350 l 10350 4350 l 10350 4500 l 9825 4500 l 9825 4350 l 9975 4350 l 9975 4050 l 9675 4050 l 9675 4200 l 9375 4200 l 9375 3975 l 9000 3975 l 9000 4200 l 8775 4200 l 8775 4500 l 8625 4500 l 8625 4800 l 8400 4800 l 7950 4800 l 7950 4575 l 8250 4575 l 8250 4050 l 7800 4050 l 7800 4125 l 8025 4125 l 8025 4425 l 7650 4425 l 7650 4350 l 7875 4350 l 7875 4275 l 7350 4275 l 7350 4500 l 6900 4500 l 6900 4350 l 7050 4350 l 7050 3975 l 6750 3975 l 6750 4200 l 6300 4200 l 6300 4425 l 6450 4425 l 6450 4650 l 6150 4650 l 6150 4800 l 6000 4800 l 5775 4800 l 5775 4650 l 5550 4650 l 5550 4500 l 5400 4500 l 5400 4650 l 4875 4650 l 4875 4575 l 5025 4575 l 5025 4350 l 4875 4350 l 4875 4425 l 4050 4425 l 4050 4500 l 4125 4500 l 4125 4650 l 3675 4650 l 3675 4800 l 3600 4800 l 3375 4800 l 3375 4575 l 2850 4575 l 2850 4425 l 2475 4425 l 2475 4275 l 2775 4275 l 2775 4125 l 3300 4125 l 3300 3975 l 3000 3975 l 3000 3825 l 2250 3825 l 2250 3975 l 2475 3975 l 2475 4125 l 2025 4125 l 2025 3975 l 1500 3975 l 1500 4275 l 1575 4275 l 1575 4125 l 1725 4125 l 1725 4425 l 1575 4425 l 1575 4500 l 1425 4500 l 1425 4800 l 1200 4800 l gs col4 s gr 7.500 slw % Ellipse n 3600 4800 50 50 0 360 DrawEllipse gs col1 1.00 shd ef gr gs col1 s gr % Ellipse n 6000 4800 50 50 0 360 DrawEllipse gs col1 1.00 shd ef gr gs col1 s gr % Ellipse n 8400 4800 50 50 0 360 DrawEllipse gs col1 1.00 shd ef gr gs col1 s gr % Ellipse n 10800 4800 50 50 0 360 DrawEllipse gs col1 1.00 shd ef gr gs col1 s gr % Ellipse n 13200 4800 50 50 0 360 DrawEllipse gs col1 1.00 shd ef gr gs col1 s gr % Ellipse n 1200 4800 50 50 0 360 DrawEllipse gs col1 1.00 shd ef gr gs col1 s gr $F2psEnd rs %%EndDocument @endspecial 0 0 0 TeXcolorrgb 2410 296 a Fh(R)2556 322 y Fg(2)p Black 0 0 0 TeXcolorrgb 1510 858 a Ff(a)1599 884 y Fg(1)p Black 0 0 0 TeXcolorrgb 310 858 a Ff(a)399 884 y Fg(0)p Black 0 0 0 TeXcolorrgb 2710 858 a Ff(a)2799 884 y Fg(2)p Black 0 0 0 TeXcolorrgb 6310 858 a Ff(a)6399 884 y Fe(M)p Black 310 912 a currentpoint currentpoint translate 1 0.53383 div 1 0.53383 div scale neg exch neg exch translate 310 912 a Black 1055 1095 a FB(Figure)27 b(2:)37 b(The)27 b(restricted)g(family)h(of)f(op)r(en)h (con)n(tours.)p Black Black 515 1360 a(\()p FA(a)591 1372 y Fz(k)q Fv(\000)p Fx(1)744 1360 y FB(and)g FA(a)950 1372 y Fz(k)1018 1360 y FB(are)f(th)n(us)h(the)f(b)r(ottom)h(corners)e (of)i(the)g(rectangle)e Fy(R)2725 1372 y Fz(k)2766 1360 y FB(\).)639 1460 y(W)-7 b(e)31 b(further)g(restrict)f(the)h(summation) f(to)h(the)g(set)f(of)h(op)r(en)f(con)n(tours)f FA(\015)36 b FB(satisfying)515 1560 y(the)28 b(follo)n(wing)e(conditions)h(\(see)h (Fig.)f(2\):)p Black 639 1726 a Fy(\017)p Black 41 w FA(\015)h FB(=)23 b FA(\021)922 1738 y Fx(1)977 1726 y Fy(q)c FA(\021)1099 1738 y Fx(2)1155 1726 y Fy(q)g(\001)14 b(\001)g(\001)k(q)h FA(\021)1473 1738 y Fz(M)1547 1726 y FB(.)p Black 639 1892 a Fy(\017)p Black 41 w FB(The)25 b(piece)f FA(\021)1135 1904 y Fz(k)1176 1892 y FB(,)h FA(k)h FB(=)c(1)p FA(;)14 b(:)g(:)g(:)f(;)h(M)9 b FB(,)25 b(use)f(only)g(inner)g(edges)f(of)h(the)h FA(k)s FB(th)g(rectangle,)e (and)722 1991 y(connects)k FA(a)1103 2003 y Fz(k)q Fv(\000)p Fx(1)1257 1991 y FB(and)g FA(a)1462 2003 y Fz(k)1503 1991 y FB(.)515 2157 y(By)h(\(A.15\))g(and)f(\(A.14\),)1563 2338 y FA(q)1600 2350 y Fz(N)1664 2338 y FB(\()p FA(\015)5 b FB(\))23 b Fy(\025)1912 2234 y Fz(M)1894 2259 y Fw(Y)1886 2438 y Fz(k)q Fx(=1)2021 2338 y FA(q)2058 2350 y Fx(s)p Fz(:)p Fx(i)p Fz(:)2147 2338 y FB(\()p FA(\021)2220 2350 y Fz(k)2261 2338 y FB(\))14 b FA(:)515 2562 y FB(Therefore)1382 2643 y Fw(X)1349 2821 y Fz(\015)t Fv(\032S)1481 2829 y Fn(H)1548 2722 y FA(q)1585 2734 y Fz(N)1648 2722 y FB(\()p FA(\015)5 b FB(\))23 b Fy(\025)1897 2618 y Fz(M)1878 2643 y Fw(Y)1871 2822 y Fz(k)q Fx(=1)2053 2643 y Fw(X)2006 2821 y Fz(\021)2040 2830 y Fu(k)2076 2821 y Fv(\032R)2185 2830 y Fu(k)2235 2722 y FA(q)2272 2734 y Fx(s)p Fz(:)p Fx(i)p Fz(:)2361 2722 y FB(\()p FA(\021)2434 2734 y Fz(k)2475 2722 y FB(\))14 b(;)515 2957 y(the)39 b(last)f(summation)h(runs)g(o)n (v)n(er)e(con)n(tours)g(satisfying)h(the)h(condition)g(ab)r(o)n(v)n(e.) 69 b(It)39 b(is)515 3056 y(con)n(trolled)26 b(thanks)h(to)h(\(A.17\),)g (whic)n(h)f(implies)h(that)1267 3177 y Fw(X)1219 3355 y Fz(\021)1253 3364 y Fu(k)1289 3355 y Fv(\032R)1398 3364 y Fu(k)1448 3256 y FA(q)1485 3268 y Fx(s.i.)1572 3256 y FB(\()p FA(\021)1645 3268 y Fz(k)1687 3256 y FB(\))23 b Fy(\025)g(H)1901 3221 y Fv(\000)p Fz(C)2159 3177 y Fw(X)2045 3356 y Fz(\020)t Fx(:)11 b Fz(a)2145 3365 y Fu(k)q Fn(\000)p Fm(1)2255 3356 y Fv(!)p Fz(a)2357 3365 y Fu(k)2407 3256 y FA(q)2444 3268 y Fx(s.i.)2531 3256 y FB(\()p FA(\020)6 b FB(\))14 b FA(;)515 3533 y FB(pro)n(vided)26 b FA(K)33 b FB(is)28 b(big)f(enough.)37 b(W)-7 b(e)27 b(then)i(com)n(bine)e(\(A.13\))g(and)h(\(A.23\))f(to)h(obtain)1087 3654 y Fw(X)973 3832 y Fz(\020)t Fx(:)11 b Fz(a)1073 3841 y Fu(k)q Fn(\000)p Fm(1)1183 3832 y Fv(!)p Fz(a)1285 3841 y Fu(k)1335 3732 y FA(q)1372 3744 y Fx(s.i.)1459 3732 y FB(\()p FA(\020)6 b FB(\))24 b Fy(\025)f FA(C)d Fy(j)p FA(a)1823 3744 y Fz(k)q Fv(\000)p Fx(1)1967 3732 y Fy(\000)e FA(a)2094 3744 y Fz(k)2135 3732 y Fy(j)2158 3698 y Fv(\000)p Fx(3)p Fz(=)p Fx(2)2328 3732 y FA(e)2367 3698 y Fv(\000)p Fz(\034)2450 3707 y Fu(\014)2488 3698 y Fx(\()p Fd(e)2548 3706 y Fm(1)2581 3698 y Fx(\))p Fv(j)p Fz(a)2663 3707 y Fu(k)q Fn(\000)p Fm(1)2772 3698 y Fv(\000)p Fz(a)2860 3707 y Fu(k)2897 3698 y Fv(j)1589 3967 y Fy(\025)23 b FA(C)d Fy(H)1827 3933 y Fv(\000)p Fx(3)1930 3967 y FA(e)1969 3933 y Fv(\000)p Fz(\034)2052 3942 y Fu(\014)2090 3933 y Fx(\()p Fd(e)2150 3941 y Fm(1)2183 3933 y Fx(\))11 b Fv(j)p Fz(a)2276 3942 y Fu(k)q Fn(\000)p Fm(1)2385 3933 y Fv(\000)p Fz(a)2473 3942 y Fu(k)2510 3933 y Fv(j)2547 3967 y FA(;)515 4150 y FB(where)25 b FA(\034)789 4162 y Fz(\014)834 4150 y FB(\()p Fp(e)910 4162 y Fx(1)947 4150 y FB(\))h(is)g(the)g(surface)f(tension)h(in)g(the)g(horizon)n(tal) e(direction.)36 b(Since,)26 b(b)n(y)h(\(A.11\))515 4250 y(\(with)h FA(\025)c FB(=)e(0\))28 b(and)f(\(A.12\))h(,)f(\(A.13\))h (and)g(\(A.23\))o(,)1544 4475 y FA(e)1583 4440 y Fv(\000)p Fz(\034)1666 4449 y Fu(\014)1705 4440 y Fx(\()p Fd(e)1765 4448 y Fm(1)1797 4440 y Fx(\))12 b Fz(N)1921 4475 y Fy(\025)2018 4418 y FA(Z)2075 4430 y Fv(\006)p Fz(;)p Fx(0)p Fz(;)p Fx(\003)2245 4438 y Fu(N)p 2018 4456 285 4 v 2018 4532 a FA(Z)2075 4544 y Fx(+)p Fz(;)p Fx(0)p Fz(;)p Fx(\003)2244 4552 y Fu(N)2326 4475 y FA(;)515 4704 y FB(the)28 b(conclusion)e(follo) n(ws.)p 1392 4704 42 42 v Black Black eop end %%Page: 19 19 TeXDict begin 19 18 bop Black 515 232 a Fr(En)n(tropic)22 b(repulsion)g(in)f(external)h(\014eld;)g(v)n(ersion)f(from)g(July)g(3,) f(2003)1118 b FB(19)p Black 515 523 a Fp(2.3.2)93 b(Pro)s(of)32 b(of)g(the)g(lo)m(w)m(er)f(b)s(ound)515 676 y FB(W)-7 b(e)29 b(turn)g(no)n(w)f(to)h(the)g(pro)r(of)f(of)36 b(\(1.3\))o(.)41 b(As)29 b(b)r(efore,)g(w)n(e)f(omit)h(reference)f(to)h FA(\014)k FB(and)c FA(h)g FB(in)515 776 y(the)f(notations,)f(write)h (simply)g(\003)1583 746 y Fx(+)1665 776 y FB(and)g(\003)1885 746 y Fv(\000)1941 776 y FB(,)g(and)g(also)e(set)i FA(C)2509 788 y Fz(\025;N)2655 776 y FB(=)23 b FA(\025)2791 746 y Fv(\000)p Fx(1)p Fz(=)p Fx(3)2948 776 y Fy(j)14 b FB(log)g FA(\025)p Fy(j)3177 746 y Fv(\000)p Fx(3)3280 776 y FA(N)9 b FB(.)515 876 y(W)-7 b(e)25 b(also)e(denote)i(b)n(y)f Fy(A)h FB(the)g(set)g(of)g(op)r(en)g(con)n(tours)e(suc)n(h)h(that)h Fy(j)p FB(\003)2617 845 y Fv(\000)2673 876 y Fy(j)e FA(<)g(C)2866 888 y Fz(\025;N)2988 876 y FB(.)36 b(Applying)515 975 y(Lemma)27 b(3)g(yields)746 1180 y FA(\026)796 1192 y Fv(\006)p Fz(;\025;)p Fx(\003)972 1200 y Fu(N)1029 1180 y FB(\()p Fy(A)p FB(\))d Fy(\024)f FA(e)1310 1146 y Fz(C)15 b(\025)1412 1121 y Fm(2)p Fu(=)p Fm(3)1503 1146 y Fv(j)c Fx(log)h Fz(\025)p Fv(j)1690 1121 y Fm(2)1734 1146 y Fz(N)1831 1124 y FA(Z)1888 1136 y Fx(+)p Fz(;)p Fx(0)p Fz(;)p Fx(\003)2057 1144 y Fu(N)p 1830 1161 285 4 v 1830 1237 a FA(Z)1887 1249 y Fv(\006)p Fz(;)p Fx(0)p Fz(;)p Fx(\003)2057 1257 y Fu(N)2169 1101 y Fw(X)2161 1279 y Fz(\015)t Fv(2A)2312 1180 y FA(w)r FB(\()p FA(\015)5 b FB(\))2518 1121 y FA(Z)2575 1137 y Fx(+)p Fz(;\025;)p Fx(\003)2750 1120 y Fm(+)2815 1121 y FA(Z)2872 1137 y Fv(\000)p Fz(;\025;)p Fx(\003)3048 1120 y Fn(\000)p 2518 1161 583 4 v 2665 1237 a FA(Z)2722 1249 y Fx(+)p Fz(;\025;)p Fx(\003)2897 1257 y Fu(N)3125 1180 y FA(:)515 1429 y FB(Our)33 b(\014rst)g(task)g(is)g(again)f(to)i(get)f(rid)g(of)h(the)g (bulk)f(\014eld.)55 b(This)34 b(is)f(the)h(con)n(ten)n(t)f(of)h(the)515 1529 y(follo)n(wing)p Black 515 1680 a Fp(Lemma)d(4)p Black 42 w Fo(F)-6 b(or)31 b(al)t(l)h FA(\014)d(>)c(\014)1432 1692 y Fz(c)1465 1680 y Fo(,)32 b(ther)l(e)f(exists)f FA(C)2017 1692 y Fx(1)2080 1680 y FA(<)25 b Fy(1)30 b Fo(and)i FA(C)2505 1692 y Fx(2)2567 1680 y FA(>)25 b FB(0)30 b Fo(such)h(that,)h(for)g(any)515 1780 y(set)d Fy(C)34 b Fo(of)d(op)l(en)f(c)l(ontours,)608 1954 y FA(Z)665 1966 y Fx(+)p Fz(;)p Fx(0)p Fz(;)p Fx(\003)834 1974 y Fu(N)p 608 1991 285 4 v 608 2067 a FA(Z)665 2079 y Fv(\006)p Fz(;)p Fx(0)p Fz(;)p Fx(\003)835 2087 y Fu(N)940 1931 y Fw(X)939 2109 y Fz(\015)t Fv(2C)1075 2010 y FA(w)r FB(\()p FA(\015)5 b FB(\))1281 1951 y FA(Z)1338 1966 y Fx(+)p Fz(;\025;)p Fx(\003)1513 1950 y Fm(+)1578 1951 y FA(Z)1635 1966 y Fv(\000)p Fz(;\025;)p Fx(\003)1811 1950 y Fn(\000)p 1281 1991 583 4 v 1428 2067 a FA(Z)1485 2079 y Fx(+)p Fz(;\025;)p Fx(\003)1660 2087 y Fu(N)1653 2275 y Fy(\024)22 b FA(e)1779 2241 y Fz(C)1827 2249 y Fm(1)1870 2241 y Fz(\025)12 b(N)2017 2219 y FA(Z)2074 2231 y Fx(+)p Fz(;)p Fx(0)p Fz(;)p Fx(\003)2243 2239 y Fu(N)p 2017 2256 285 4 v 2017 2332 a FA(Z)2074 2344 y Fv(\006)p Fz(;)p Fx(0)p Fz(;)p Fx(\003)2244 2352 y Fu(N)2349 2196 y Fw(X)2348 2374 y Fz(\015)t Fv(2C)2484 2275 y FA(q)2521 2287 y Fz(N)2584 2275 y FB(\()p FA(\015)5 b FB(\))41 b(+)h FA(e)2883 2241 y Fv(\000)p Fz(C)2983 2249 y Fm(2)3025 2241 y Fz(N)3102 2275 y FA(:)83 b FB(\(2.7\))515 2524 y Fp(Pro)s(of)31 b(of)h(Lemma)g(4.)73 b FB(By)27 b(symmetry)-7 b(,)964 2670 y FA(Z)1021 2686 y Fx(+)p Fz(;\025;)p Fx(\003)1196 2669 y Fm(+)1261 2670 y FA(Z)1318 2686 y Fv(\000)p Fz(;\025;)p Fx(\003)1494 2669 y Fn(\000)p 964 2710 583 4 v 1111 2786 a FA(Z)1168 2798 y Fx(+)p Fz(;\025;)p Fx(\003)1343 2806 y Fu(N)1580 2729 y FB(=)1678 2670 y FA(Z)1735 2686 y Fx(+)p Fz(;)p Fv(\000)p Fz(\025;)p Fx(\003)1962 2669 y Fn(\000)p 1678 2710 338 4 v 1704 2786 a FA(Z)1761 2802 y Fx(+)p Fz(;\025;)p Fx(\003)1936 2785 y Fn(\000)2048 2729 y FA(\026)2098 2741 y Fx(+)p Fz(;\025;)p Fx(\003)2273 2749 y Fu(N)2331 2729 y FB(\()p FA(\033)2410 2741 y Fz(x)2475 2729 y FB(=)23 b(1)p FA(;)k Fy(8)p FA(x)d Fy(\030)e FA(\015)5 b FB(\))1580 2916 y Fy(\024)23 b FA(\026)1718 2928 y Fx(+)p Fz(;\025;)p Fx(\003)1893 2936 y Fu(N)1951 2916 y FB(\()p FA(\033)2030 2928 y Fz(x)2095 2916 y FB(=)g(1)p FA(;)k Fy(8)p FA(x)d Fy(\030)e FA(\015)5 b FB(\))14 b FA(;)515 3080 y FB(where)27 b(as)g(b)r(efore)g FA(x)d Fy(\030)e FA(\015)32 b FB(if)d(its)e(v)-5 b(alue)28 b(is)f(completely)h(determined)f(b)n(y)h FA(\015)5 b FB(,)27 b(and)h(w)n(e)f(used)776 3255 y FA(Z)833 3271 y Fx(+)p Fz(;)p Fv(\000)p Fz(\025;)p Fx(\003)1060 3254 y Fn(\000)p 776 3295 V 802 3371 a FA(Z)859 3387 y Fx(+)p Fz(;\025;)p Fx(\003)1034 3370 y Fn(\000)1146 3314 y FB(=)22 b(exp)1374 3172 y Fw(\()1469 3236 y(X)1441 3418 y Fz(x)p Fv(2)p Fx(\003)1569 3402 y Fn(\000)1632 3201 y Fw(Z)1715 3222 y Fz(\025)1678 3390 y Fx(0)1772 3247 y Fw(\000)1810 3314 y Fy(h)p FA(\033)1889 3326 y Fz(x)1932 3314 y Fy(i)1964 3330 y Fx(+)p Fz(;)p Fv(\000)p Fz(s;)p Fx(\003)2183 3314 y Fn(\000)27 b Fy(\000)18 b(h)p FA(\033)2417 3326 y Fz(x)2459 3314 y Fy(i)2491 3330 y Fx(+)p Fz(;s;)p Fx(\003)2658 3314 y Fn(\000)2712 3247 y Fw(\001)2787 3314 y FB(d)p FA(s)2872 3172 y Fw(\))2962 3314 y Fy(\024)23 b FB(1)14 b FA(:)515 3560 y FB(No)n(w,)598 3750 y FA(\026)648 3762 y Fx(+)p Fz(;\025;)p Fx(\003)823 3770 y Fu(N)880 3750 y FB(\()p FA(\033)959 3762 y Fz(x)1025 3750 y FB(=)23 b(1)p FA(;)k Fy(8)p FA(x)d Fy(\030)e FA(\015)5 b FB(\))23 b(=)g FA(\026)1650 3762 y Fx(+)p Fz(;)p Fx(0)p Fz(;)p Fx(\003)1819 3770 y Fu(N)1876 3750 y FB(\()p FA(\033)1955 3762 y Fz(x)2021 3750 y FB(=)f(1)p FA(;)28 b Fy(8)p FA(x)23 b Fy(\030)g FA(\015)5 b FB(\))935 3958 y Fy(\002)18 b FB(exp)1158 3816 y Fw(\()1256 3879 y(X)1225 4057 y Fz(x)p Fv(2)p Fx(\003)1353 4065 y Fu(N)1420 3845 y Fw(Z)1503 3865 y Fz(\025)1466 4034 y Fx(0)1547 3891 y Fw(\000)1585 3958 y Fy(h)p FA(\033)1664 3970 y Fz(x)1720 3958 y Fy(j)c FA(\033)1804 3970 y Fz(y)1867 3958 y FB(=)23 b(1)p FA(;)k Fy(8)p FA(y)f Fy(\030)d FA(\015)5 b Fy(i)2328 3970 y Fx(+)p Fz(;s;)p Fx(\003)2495 3978 y Fu(N)2571 3958 y Fy(\000)18 b(h)p FA(\033)2733 3970 y Fz(x)2775 3958 y Fy(i)2807 3970 y Fx(+)p Fz(;s;)p Fx(\003)2974 3978 y Fu(N)3032 3891 y Fw(\001)3093 3958 y FB(d)p FA(s)3178 3816 y Fw(\))3273 3958 y FA(:)515 4209 y FB(The)k(di\013erence)g(in)h (the)f(exp)r(onen)n(t)h(can)f(easily)f(b)r(e)i(b)r(ounded)f(using)h (\(A.26\):)35 b(There)21 b(exists)515 4308 y FA(C)29 b(<)23 b Fy(1)k FB(suc)n(h)h(that,)g(uniformly)f(in)h FA(s)23 b Fy(\025)g FB(0,)857 4485 y Fy(h)p FA(\033)936 4497 y Fz(x)993 4485 y Fy(j)14 b FA(\033)1077 4497 y Fz(y)1140 4485 y FB(=)23 b(1)p FA(;)k Fy(8)p FA(y)f Fy(\030)c FA(\015)5 b Fy(i)1600 4497 y Fx(+)p Fz(;s;)p Fx(\003)1767 4505 y Fu(N)1843 4485 y Fy(\000)18 b(h)p FA(\033)2005 4497 y Fz(x)2048 4485 y Fy(i)2080 4497 y Fx(+)p Fz(;s;)p Fx(\003)2247 4505 y Fu(N)2328 4485 y Fy(\024)23 b FA(C)2520 4406 y Fw(X)2518 4580 y Fz(z)r Fv(\030)p Fz(\015)2656 4485 y FA(e)2695 4450 y Fv(\000j)p Fz(x)p Fv(\000)p Fz(z)r Fv(j)p Fz(=C)3013 4485 y FA(;)515 4730 y FB(and)k(therefore)603 4857 y Fw(X)599 5035 y Fz(x)p Fv(2)p Fx(\003)741 4823 y Fw(Z)824 4843 y Fz(\025)787 5011 y Fx(0)868 4869 y Fw(\000)906 4936 y Fy(h)p FA(\033)985 4948 y Fz(x)1041 4936 y Fy(j)14 b FA(\033)1125 4948 y Fz(y)1188 4936 y FB(=)23 b(1)p FA(;)k Fy(8)p FA(y)f Fy(\030)d FA(\015)5 b Fy(i)1649 4948 y Fx(+)p Fz(;s;)p Fx(\003)1816 4956 y Fu(N)1892 4936 y Fy(\000)18 b(h)p FA(\033)2054 4948 y Fz(x)2096 4936 y Fy(i)2128 4948 y Fx(+)p Fz(;s;)p Fx(\003)2295 4956 y Fu(N)2353 4869 y Fw(\001)2405 4936 y FB(d)p FA(s)23 b Fy(\024)g FA(C)2666 4902 y Fv(0)2703 4936 y FA(\025)14 b FB(#)p Fy(f)p FA(z)40 b FB(:)d FA(z)27 b Fy(\030)22 b FA(\015)5 b Fy(g)14 b FA(:)p Black Black eop end %%Page: 20 20 TeXDict begin 20 19 bop Black 515 232 a Fr(En)n(tropic)22 b(repulsion)g(in)f(external)h(\014eld;)g(v)n(ersion)f(from)g(July)g(3,) f(2003)1118 b FB(20)p Black 515 523 a(W)-7 b(e)28 b(are)f(almost)g (done.)37 b(Observ)n(e)26 b(no)n(w)h(that)h(#)p Fy(f)p FA(z)40 b FB(:)d FA(z)27 b Fy(\030)c FA(\015)5 b Fy(g)22 b FA(<)h FB(4)p Fy(j)p FA(\015)5 b Fy(j)p FB(.)37 b(Let)28 b FA(K)33 b FB(b)r(e)28 b(a)f(large)515 623 y(n)n(um)n(b)r(er,)g(whic)n (h)h(will)f(b)r(e)h(c)n(hosen)f(b)r(elo)n(w.)37 b(In)27 b(the)h(case)f Fy(j)p FA(\015)5 b Fy(j)23 b FA(<)g(K)c(N)9 b FB(,)27 b(w)n(e)h(get)808 804 y FA(\026)858 816 y Fx(+)p Fz(;\025;)p Fx(\003)1033 824 y Fu(N)1091 804 y FB(\()p FA(\033)1170 816 y Fz(x)1235 804 y FB(=)23 b(1)p FA(;)k Fy(8)p FA(x)d Fy(\030)e FA(\015)5 b FB(\))23 b Fy(\024)g FA(e)1849 769 y Fx(4)p Fz(C)1934 744 y Fn(0)1956 769 y Fz(K)15 b(\025)d(N)2164 804 y FA(\026)2214 816 y Fx(+)p Fz(;)p Fx(0)p Fz(;)p Fx(\003)2383 824 y Fu(N)2440 804 y FB(\()p FA(\033)2519 816 y Fz(x)2585 804 y FB(=)22 b(1)p FA(;)28 b Fy(8)p FA(x)23 b Fy(\030)g FA(\015)5 b FB(\))14 b FA(:)515 973 y FB(This)26 b(yields)f(the)i(\014rst)e(term) h(in)h(\(2.7\))o(.)37 b(The)26 b(second)f(term)h(tak)n(es)f(care)g(of)h (the)g(remaining)515 1072 y(op)r(en)h(con)n(tours.)36 b(Indeed,)760 1250 y Fw(X)791 1414 y Fz(\015)t Fx(:)696 1477 y Fv(j)p Fz(\015)t Fv(j\025)p Fz(K)t(N)958 1329 y FA(q)995 1341 y Fz(N)1058 1329 y FB(\()p FA(\015)5 b FB(\))23 b FA(e)1232 1295 y Fz(C)t(C)1336 1270 y Fn(0)1369 1295 y Fz(\025)12 b Fv(j)p Fz(\015)t Fv(j)1525 1329 y Fy(\024)1613 1250 y Fw(X)1613 1429 y Fz(k)q Fv(\025)p Fx(0)1748 1329 y FA(e)1787 1295 y Fz(C)t(C)1891 1270 y Fn(0)1924 1295 y Fz(\025)g Fx(\()p Fz(K)t Fx(+)p Fz(k)q Fx(+1\))f Fz(N)2369 1218 y Fx(\()p Fz(K)t Fx(+)p Fz(k)q Fx(+1\))h Fz(N)6 b Fv(\000)p Fx(1)2529 1250 y Fw(X)2418 1432 y Fz(l)p Fx(=\()p Fz(K)t Fx(+)p Fz(k)q Fx(\))12 b Fz(N)2837 1250 y Fw(X)2868 1414 y Fz(\015)t Fx(:)2822 1477 y Fv(j)p Fz(\015)t Fv(j)p Fx(=)p Fz(l)2986 1329 y FA(q)3023 1341 y Fz(N)3086 1329 y FB(\()p FA(\015)5 b FB(\))1525 1620 y Fy(\024)1613 1541 y Fw(X)1613 1720 y Fz(k)q Fv(\025)p Fx(0)1748 1620 y FA(e)1787 1586 y Fv(\000)p Fz(C)1891 1561 y Fn(00)1931 1586 y Fx(\()p Fz(K)t Fx(+)p Fz(k)q Fx(\))12 b Fz(N)1525 1855 y Fy(\024)23 b FA(e)1652 1820 y Fv(\000)p Fz(C)1756 1795 y Fn(000)1814 1820 y Fz(K)15 b(N)1962 1855 y FA(;)515 2024 y FB(where)27 b(w)n(e)g(used)h(\(A.22\).)36 b(Consequen)n(tly)-7 b(,)27 b(since)1444 2179 y FA(Z)1501 2191 y Fx(+)p Fz(;)p Fx(0)p Fz(;)p Fx(\003)1670 2199 y Fu(N)p 1444 2216 285 4 v 1444 2292 a FA(Z)1501 2304 y Fv(\006)p Fz(;)p Fx(0)p Fz(;)p Fx(\003)1671 2312 y Fu(N)1761 2235 y Fy(\024)22 b FA(C)f(N)2004 2201 y Fx(3)p Fz(=)p Fx(2)2122 2235 y FA(e)2161 2201 y Fz(\034)2192 2210 y Fu(\014)2230 2201 y Fx(\()p Fd(e)2290 2209 y Fm(1)2323 2201 y Fx(\))11 b Fz(N)2437 2235 y FA(;)515 2451 y FB(w)n(e)27 b(see)g(that)1034 2589 y FA(Z)1091 2601 y Fx(+)p Fz(;)p Fx(0)p Fz(;)p Fx(\003)1260 2609 y Fu(N)p 1033 2626 V 1033 2702 a FA(Z)1090 2714 y Fv(\006)p Fz(;)p Fx(0)p Fz(;)p Fx(\003)1260 2722 y Fu(N)1469 2566 y Fw(X)1364 2748 y Fz(\015)t Fx(:)11 b Fv(j)p Fz(\015)t Fv(j\025)p Fz(K)j(N)1707 2645 y FA(w)r FB(\()p FA(\015)5 b FB(\))1913 2586 y FA(Z)1970 2601 y Fx(+)p Fz(;\025;)p Fx(\003)2145 2585 y Fm(+)2210 2586 y FA(Z)2267 2601 y Fv(\000)p Fz(;\025;)p Fx(\003)2443 2585 y Fn(\000)p 1913 2626 583 4 v 2060 2702 a FA(Z)2117 2714 y Fx(+)p Fz(;\025;)p Fx(\003)2292 2722 y Fu(N)2529 2645 y Fy(\024)23 b FA(e)2656 2611 y Fv(\000)p Fz(C)14 b(N)2847 2645 y FA(;)515 2906 y FB(pro)n(vided)26 b FA(K)33 b FB(is)28 b(c)n(hosen)f(large)f(enough.) p 1859 2906 42 42 v 639 3050 a(Applying)i(the)g(lemma,)g(w)n(e)f(ha)n (v)n(e)805 3257 y FA(\026)855 3269 y Fv(\006)p Fz(;\025;)p Fx(\003)1031 3277 y Fu(N)1088 3257 y FB(\()p Fy(A)p FB(\))d Fy(\024)f FA(e)1369 3223 y Fz(C)14 b(\025)1470 3198 y Fm(2)p Fu(=)p Fm(3)1562 3223 y Fv(j)d Fx(log)h Fz(\025)p Fv(j)1749 3198 y Fm(2)1793 3223 y Fz(N)1890 3201 y FA(Z)1947 3213 y Fx(+)p Fz(;)p Fx(0)p Fz(;)p Fx(\003)2116 3221 y Fu(N)p 1889 3238 285 4 v 1889 3314 a FA(Z)1946 3326 y Fv(\006)p Fz(;)p Fx(0)p Fz(;)p Fx(\003)2116 3334 y Fu(N)2330 3178 y Fw(X)2362 3342 y Fz(\015)t Fx(:)2220 3414 y Fv(j)p Fx(\003)2285 3389 y Fn(\000)2334 3414 y Fv(j)p Fz()g FB(0,)k(and)f(so)h(w)n(e)f(are)g(left)h(with)h(estimating)e(the)i (probabilit)n(y)d(that)i Fy(j)p FB(\003)3210 3702 y Fv(\000)3266 3732 y Fy(j)c FA(<)515 3832 y(C)574 3844 y Fz(\025;N)724 3832 y FB(in)j(the)g(absence)f(of)g(bulk)h(magnetic)f(\014eld,)h(a)f (purely)g(en)n(tropic)g(problem.)639 3931 y(The)h(next)g(step)h(is)e (to)h(observ)n(e)f(that)h(the)g(ev)n(en)n(t)g Fy(fj)p FB(\003)2322 3901 y Fv(\000)2377 3931 y Fy(j)c FA(<)f(C)2571 3943 y Fz(\025;N)2693 3931 y Fy(g)28 b FB(is)g(increasing.)36 b(So,)515 4031 y(b)n(y)27 b(FK)n(G)g(inequalities,)1116 4200 y FA(\026)1166 4212 y Fv(\006)p Fz(;)p Fx(0)p Fz(;)p Fx(\003)1336 4220 y Fu(N)1394 4200 y FB(\()p Fy(j)p FB(\003)1507 4166 y Fv(\000)1563 4200 y Fy(j)c FA(<)g(C)1756 4212 y Fz(\025;N)1878 4200 y FB(\))g Fy(\024)g FA(\026)2071 4212 y Fv(\006)p Fz(;)p Fx(0)p Fz(;)p Fx(\012)2247 4200 y FB(\()p Fy(j)p FB(\003)2360 4166 y Fv(\000)2416 4200 y Fy(j)g FA(<)g(C)2609 4212 y Fz(\025;N)2731 4200 y FB(\))515 4369 y(where)k(\012)g(is)h(the)g(b)r(o)n(x)f(\(see)h(Fig.)f(3\))848 4538 y(\012)c(=)g(\003)1077 4550 y Fz(N)1158 4538 y Fy(n)18 b(f)p FA(z)25 b FB(:)37 b FA(z)1423 4550 y Fx(1)1483 4538 y FB(=)23 b Fy(\000)p FA(N)r(=)p FB(2)17 b(+)h(1)g(+)g FA(k)s FB([)p FA(A\025)2211 4504 y Fv(\000)p Fx(2)p Fz(=)p Fx(3)2368 4538 y Fy(j)c FB(log)g FA(\025)p Fy(j)2597 4504 y Fv(\000)p Fx(2)2686 4538 y FB(])p FA(;)28 b(k)e Fy(2)d Fq(N)p Fy(g)14 b FA(;)515 4707 y(A)23 b FB(b)r(eing)g(a)g(small) g(n)n(um)n(b)r(er)g(to)g(b)r(e)h(c)n(hosen)e(later.)35 b(Let)23 b(us)g(denote)g(b)n(y)g(\003)2765 4672 y Fv(\000)2765 4732 y Fz(k)2844 4707 y FB(the)g(comp)r(onen)n(t)515 4807 y(of)34 b(\003)674 4777 y Fv(\000)763 4807 y FB(con)n(tained)f(in) h(the)h FA(k)s FB(th)f(slice)f(\012)1802 4819 y Fz(k)1877 4807 y FB(of)h(\012.)55 b(Let)34 b FA(K)2342 4819 y Fz(\025)2419 4807 y FB(=)f FA(\025)2565 4777 y Fv(\000)p Fx(1)2654 4807 y Fy(j)14 b FB(log)g FA(\025)p Fy(j)2883 4777 y Fv(\000)p Fx(9)p Fz(=)p Fx(2)3040 4807 y FB(.)56 b(W)-7 b(e)34 b(are)515 4907 y(going)26 b(to)i(sho)n(w)e(that)1457 5006 y FA(\026)1507 5018 y Fv(\006)p Fz(;)p Fx(0)p Fz(;)p Fx(\012)1679 5026 y Fm(1)1715 5006 y FB(\()p Fy(j)p FB(\003)1828 4971 y Fv(\000)1828 5028 y Fx(1)1884 5006 y Fy(j)e FA(<)e(K)2089 5018 y Fz(\025)2132 5006 y FB(\))i FA(<)e FB(7)p FA(=)p FB(8)14 b FA(:)770 b FB(\(2.8\))p Black Black eop end %%Page: 21 21 TeXDict begin 21 20 bop Black 515 232 a Fr(En)n(tropic)22 b(repulsion)g(in)f(external)h(\014eld;)g(v)n(ersion)f(from)g(July)g(3,) f(2003)1118 b FB(21)p Black Black 788 1267 a currentpoint currentpoint translate 0.38373 0.38373 scale neg exch neg exch translate 788 1267 a @beginspecial 0 @llx 0 @lly 722 @urx 259 @ury 7220 @rwi @setspecial %%BeginDocument: Omega.pstex %!PS-Adobe-2.0 EPSF-2.0 %%Title: Omega.pstex %%Creator: fig2dev Version 3.2 Patchlevel 3d %%CreationDate: Mon Jul 1 10:49:14 2002 %%For: velenik@eupalidos.cmi.univ-mrs.fr (Yvan VELENIK, CR probabilites) %%BoundingBox: 0 0 722 259 %%Magnification: 1.0000 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save newpath 0 259 moveto 0 0 lineto 722 0 lineto 722 259 lineto closepath clip newpath -53.3 306.7 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def $F2psBegin 10 setmiterlimit 0.06000 0.06000 sc % % Fig objects follow % % Polyline 15.000 slw n 2025 900 m 2175 900 l gs col4 s gr % Polyline n 2100 825 m 2100 975 l gs col4 s gr % Polyline n 2025 1200 m 2175 1200 l gs col4 s gr % Polyline n 2100 1125 m 2100 1275 l gs col4 s gr % Polyline n 2025 1500 m 2175 1500 l gs col4 s gr % Polyline n 2100 1425 m 2100 1575 l gs col4 s gr % Polyline n 2025 1800 m 2175 1800 l gs col4 s gr % Polyline n 2100 1725 m 2100 1875 l gs col4 s gr % Polyline n 2025 2100 m 2175 2100 l gs col4 s gr % Polyline n 2100 2025 m 2100 2175 l gs col4 s gr % Polyline n 2025 2400 m 2175 2400 l gs col4 s gr % Polyline n 2100 2325 m 2100 2475 l gs col4 s gr % Polyline n 2025 2700 m 2175 2700 l gs col4 s gr % Polyline n 2100 2625 m 2100 2775 l gs col4 s gr % Polyline n 2025 3000 m 2175 3000 l gs col4 s gr % Polyline n 2100 2925 m 2100 3075 l gs col4 s gr % Polyline n 2025 3300 m 2175 3300 l gs col4 s gr % Polyline n 2100 3225 m 2100 3375 l gs col4 s gr % Polyline n 2025 3600 m 2175 3600 l gs col4 s gr % Polyline n 2100 3525 m 2100 3675 l gs col4 s gr % Polyline n 2025 3900 m 2175 3900 l gs col4 s gr % Polyline n 2100 3825 m 2100 3975 l gs col4 s gr % Polyline n 2025 4200 m 2175 4200 l gs col4 s gr % Polyline n 2100 4125 m 2100 4275 l gs col4 s gr % Polyline n 2025 4500 m 2175 4500 l gs col4 s gr % Polyline n 2100 4425 m 2100 4575 l gs col4 s gr % Polyline n 2025 4800 m 2175 4800 l gs col4 s gr % Polyline n 2100 4725 m 2100 4875 l gs col4 s gr % Polyline n 3225 900 m 3375 900 l gs col4 s gr % Polyline n 3300 825 m 3300 975 l gs col4 s gr % Polyline n 3225 1200 m 3375 1200 l gs col4 s gr % Polyline n 3300 1125 m 3300 1275 l gs col4 s gr % Polyline n 3225 1500 m 3375 1500 l gs col4 s gr % Polyline n 3300 1425 m 3300 1575 l gs col4 s gr % Polyline n 3225 1800 m 3375 1800 l gs col4 s gr % Polyline n 3300 1725 m 3300 1875 l gs col4 s gr % Polyline n 3225 2100 m 3375 2100 l gs col4 s gr % Polyline n 3300 2025 m 3300 2175 l gs col4 s gr % Polyline n 3225 2400 m 3375 2400 l gs col4 s gr % Polyline n 3300 2325 m 3300 2475 l gs col4 s gr % Polyline n 3225 2700 m 3375 2700 l gs col4 s gr % Polyline n 3300 2625 m 3300 2775 l gs col4 s gr % Polyline n 3225 3000 m 3375 3000 l gs col4 s gr % Polyline n 3300 2925 m 3300 3075 l gs col4 s gr % Polyline n 3225 3300 m 3375 3300 l gs col4 s gr % Polyline n 3300 3225 m 3300 3375 l gs col4 s gr % Polyline n 3225 3600 m 3375 3600 l gs col4 s gr % Polyline n 3300 3525 m 3300 3675 l gs col4 s gr % Polyline n 3225 3900 m 3375 3900 l gs col4 s gr % Polyline n 3300 3825 m 3300 3975 l gs col4 s gr % Polyline n 3225 4200 m 3375 4200 l gs col4 s gr % Polyline n 3300 4125 m 3300 4275 l gs col4 s gr % Polyline n 3225 4500 m 3375 4500 l gs col4 s gr % Polyline n 3300 4425 m 3300 4575 l gs col4 s gr % Polyline n 3225 4800 m 3375 4800 l gs col4 s gr % Polyline n 3300 4725 m 3300 4875 l gs col4 s gr % Polyline n 4425 900 m 4575 900 l gs col4 s gr % Polyline n 4500 825 m 4500 975 l gs col4 s gr % Polyline n 4425 1200 m 4575 1200 l gs col4 s gr % Polyline n 4500 1125 m 4500 1275 l gs col4 s gr % Polyline n 4425 1500 m 4575 1500 l gs col4 s gr % Polyline n 4500 1425 m 4500 1575 l gs col4 s gr % Polyline n 4425 1800 m 4575 1800 l gs col4 s gr % Polyline n 4500 1725 m 4500 1875 l gs col4 s gr % Polyline n 4425 2100 m 4575 2100 l gs col4 s gr % Polyline n 4500 2025 m 4500 2175 l gs col4 s gr % Polyline n 4425 2400 m 4575 2400 l gs col4 s gr % Polyline n 4500 2325 m 4500 2475 l gs col4 s gr % Polyline n 4425 2700 m 4575 2700 l gs col4 s gr % Polyline n 4500 2625 m 4500 2775 l gs col4 s gr % Polyline n 4425 3000 m 4575 3000 l gs col4 s gr % Polyline n 4500 2925 m 4500 3075 l gs col4 s gr % Polyline n 4425 3300 m 4575 3300 l gs col4 s gr % Polyline n 4500 3225 m 4500 3375 l gs col4 s gr % Polyline n 4425 3600 m 4575 3600 l gs col4 s gr % Polyline n 4500 3525 m 4500 3675 l gs col4 s gr % Polyline n 4425 3900 m 4575 3900 l gs col4 s gr % Polyline n 4500 3825 m 4500 3975 l gs col4 s gr % Polyline n 4425 4200 m 4575 4200 l gs col4 s gr % Polyline n 4500 4125 m 4500 4275 l gs col4 s gr % Polyline n 4425 4500 m 4575 4500 l gs col4 s gr % Polyline n 4500 4425 m 4500 4575 l gs col4 s gr % Polyline n 4425 4800 m 4575 4800 l gs col4 s gr % Polyline n 4500 4725 m 4500 4875 l gs col4 s gr % Polyline n 5625 900 m 5775 900 l gs col4 s gr % Polyline n 5700 825 m 5700 975 l gs col4 s gr % Polyline n 5625 1200 m 5775 1200 l gs col4 s gr % Polyline n 5700 1125 m 5700 1275 l gs col4 s gr % Polyline n 5625 1500 m 5775 1500 l gs col4 s gr % Polyline n 5700 1425 m 5700 1575 l gs col4 s gr % Polyline n 5625 1800 m 5775 1800 l gs col4 s gr % Polyline n 5700 1725 m 5700 1875 l gs col4 s gr % Polyline n 5625 2100 m 5775 2100 l gs col4 s gr % Polyline n 5700 2025 m 5700 2175 l gs col4 s gr % Polyline n 5625 2400 m 5775 2400 l gs col4 s gr % Polyline n 5700 2325 m 5700 2475 l gs col4 s gr % Polyline n 5625 2700 m 5775 2700 l gs col4 s gr % Polyline n 5700 2625 m 5700 2775 l gs col4 s gr % Polyline n 5625 3000 m 5775 3000 l gs col4 s gr % Polyline n 5700 2925 m 5700 3075 l gs col4 s gr % Polyline n 5625 3300 m 5775 3300 l gs col4 s gr % Polyline n 5700 3225 m 5700 3375 l gs col4 s gr % Polyline n 5625 3600 m 5775 3600 l gs col4 s gr % Polyline n 5700 3525 m 5700 3675 l gs col4 s gr % Polyline n 5625 3900 m 5775 3900 l gs col4 s gr % Polyline n 5700 3825 m 5700 3975 l gs col4 s gr % Polyline n 5625 4200 m 5775 4200 l gs col4 s gr % Polyline n 5700 4125 m 5700 4275 l gs col4 s gr % Polyline n 5625 4500 m 5775 4500 l gs col4 s gr % Polyline n 5700 4425 m 5700 4575 l gs col4 s gr % Polyline n 5625 4800 m 5775 4800 l gs col4 s gr % Polyline n 5700 4725 m 5700 4875 l gs col4 s gr % Polyline n 6825 900 m 6975 900 l gs col4 s gr % Polyline n 6900 825 m 6900 975 l gs col4 s gr % Polyline n 6825 1200 m 6975 1200 l gs col4 s gr % Polyline n 6900 1125 m 6900 1275 l gs col4 s gr % Polyline n 6825 1500 m 6975 1500 l gs col4 s gr % Polyline n 6900 1425 m 6900 1575 l gs col4 s gr % Polyline n 6825 1800 m 6975 1800 l gs col4 s gr % Polyline n 6900 1725 m 6900 1875 l gs col4 s gr % Polyline n 6825 2100 m 6975 2100 l gs col4 s gr % Polyline n 6900 2025 m 6900 2175 l gs col4 s gr % Polyline n 6825 2400 m 6975 2400 l gs col4 s gr % Polyline n 6900 2325 m 6900 2475 l gs col4 s gr % Polyline n 6825 2700 m 6975 2700 l gs col4 s gr % Polyline n 6900 2625 m 6900 2775 l gs col4 s gr % Polyline n 6825 3000 m 6975 3000 l gs col4 s gr % Polyline n 6900 2925 m 6900 3075 l gs col4 s gr % Polyline n 6825 3300 m 6975 3300 l gs col4 s gr % Polyline n 6900 3225 m 6900 3375 l gs col4 s gr % Polyline n 6825 3600 m 6975 3600 l gs col4 s gr % Polyline n 6900 3525 m 6900 3675 l gs col4 s gr % Polyline n 6825 3900 m 6975 3900 l gs col4 s gr % Polyline n 6900 3825 m 6900 3975 l gs col4 s gr % Polyline n 6825 4200 m 6975 4200 l gs col4 s gr % Polyline n 6900 4125 m 6900 4275 l gs col4 s gr % Polyline n 6825 4500 m 6975 4500 l gs col4 s gr % Polyline n 6900 4425 m 6900 4575 l gs col4 s gr % Polyline n 6825 4800 m 6975 4800 l gs col4 s gr % Polyline n 6900 4725 m 6900 4875 l gs col4 s gr % Polyline n 8025 900 m 8175 900 l gs col4 s gr % Polyline n 8100 825 m 8100 975 l gs col4 s gr % Polyline n 8025 1200 m 8175 1200 l gs col4 s gr % Polyline n 8100 1125 m 8100 1275 l gs col4 s gr % Polyline n 8025 1500 m 8175 1500 l gs col4 s gr % Polyline n 8100 1425 m 8100 1575 l gs col4 s gr % Polyline n 8025 1800 m 8175 1800 l gs col4 s gr % Polyline n 8100 1725 m 8100 1875 l gs col4 s gr % Polyline n 8025 2100 m 8175 2100 l gs col4 s gr % Polyline n 8100 2025 m 8100 2175 l gs col4 s gr % Polyline n 8025 2400 m 8175 2400 l gs col4 s gr % Polyline n 8100 2325 m 8100 2475 l gs col4 s gr % Polyline n 8025 2700 m 8175 2700 l gs col4 s gr % Polyline n 8100 2625 m 8100 2775 l gs col4 s gr % Polyline n 8025 3000 m 8175 3000 l gs col4 s gr % Polyline n 8100 2925 m 8100 3075 l gs col4 s gr % Polyline n 8025 3300 m 8175 3300 l gs col4 s gr % Polyline n 8100 3225 m 8100 3375 l gs col4 s gr % Polyline n 8025 3600 m 8175 3600 l gs col4 s gr % Polyline n 8100 3525 m 8100 3675 l gs col4 s gr % Polyline n 8025 3900 m 8175 3900 l gs col4 s gr % Polyline n 8100 3825 m 8100 3975 l gs col4 s gr % Polyline n 8025 4200 m 8175 4200 l gs col4 s gr % Polyline n 8100 4125 m 8100 4275 l gs col4 s gr % Polyline n 8025 4500 m 8175 4500 l gs col4 s gr % Polyline n 8100 4425 m 8100 4575 l gs col4 s gr % Polyline n 8025 4800 m 8175 4800 l gs col4 s gr % Polyline n 8100 4725 m 8100 4875 l gs col4 s gr % Polyline n 9225 900 m 9375 900 l gs col4 s gr % Polyline n 9300 825 m 9300 975 l gs col4 s gr % Polyline n 9225 1200 m 9375 1200 l gs col4 s gr % Polyline n 9300 1125 m 9300 1275 l gs col4 s gr % Polyline n 9225 1500 m 9375 1500 l gs col4 s gr % Polyline n 9300 1425 m 9300 1575 l gs col4 s gr % Polyline n 9225 1800 m 9375 1800 l gs col4 s gr % Polyline n 9300 1725 m 9300 1875 l gs col4 s gr % Polyline n 9225 2100 m 9375 2100 l gs col4 s gr % Polyline n 9300 2025 m 9300 2175 l gs col4 s gr % Polyline n 9225 2400 m 9375 2400 l gs col4 s gr % Polyline n 9300 2325 m 9300 2475 l gs col4 s gr % Polyline n 9225 2700 m 9375 2700 l gs col4 s gr % Polyline n 9300 2625 m 9300 2775 l gs col4 s gr % Polyline n 9225 3000 m 9375 3000 l gs col4 s gr % Polyline n 9300 2925 m 9300 3075 l gs col4 s gr % Polyline n 9225 3300 m 9375 3300 l gs col4 s gr % Polyline n 9300 3225 m 9300 3375 l gs col4 s gr % Polyline n 9225 3600 m 9375 3600 l gs col4 s gr % Polyline n 9300 3525 m 9300 3675 l gs col4 s gr % Polyline n 9225 3900 m 9375 3900 l gs col4 s gr % Polyline n 9300 3825 m 9300 3975 l gs col4 s gr % Polyline n 9225 4200 m 9375 4200 l gs col4 s gr % Polyline n 9300 4125 m 9300 4275 l gs col4 s gr % Polyline n 9225 4500 m 9375 4500 l gs col4 s gr % Polyline n 9300 4425 m 9300 4575 l gs col4 s gr % Polyline n 9225 4800 m 9375 4800 l gs col4 s gr % Polyline n 9300 4725 m 9300 4875 l gs col4 s gr % Polyline n 10425 900 m 10575 900 l gs col4 s gr % Polyline n 10500 825 m 10500 975 l gs col4 s gr % Polyline n 10425 1200 m 10575 1200 l gs col4 s gr % Polyline n 10500 1125 m 10500 1275 l gs col4 s gr % Polyline n 10425 1500 m 10575 1500 l gs col4 s gr % Polyline n 10500 1425 m 10500 1575 l gs col4 s gr % Polyline n 10425 1800 m 10575 1800 l gs col4 s gr % Polyline n 10500 1725 m 10500 1875 l gs col4 s gr % Polyline n 10425 2100 m 10575 2100 l gs col4 s gr % Polyline n 10500 2025 m 10500 2175 l gs col4 s gr % Polyline n 10425 2400 m 10575 2400 l gs col4 s gr % Polyline n 10500 2325 m 10500 2475 l gs col4 s gr % Polyline n 10425 2700 m 10575 2700 l gs col4 s gr % Polyline n 10500 2625 m 10500 2775 l gs col4 s gr % Polyline n 10425 3000 m 10575 3000 l gs col4 s gr % Polyline n 10500 2925 m 10500 3075 l gs col4 s gr % Polyline n 10425 3300 m 10575 3300 l gs col4 s gr % Polyline n 10500 3225 m 10500 3375 l gs col4 s gr % Polyline n 10425 3600 m 10575 3600 l gs col4 s gr % Polyline n 10500 3525 m 10500 3675 l gs col4 s gr % Polyline n 10425 3900 m 10575 3900 l gs col4 s gr % Polyline n 10500 3825 m 10500 3975 l gs col4 s gr % Polyline n 10425 4200 m 10575 4200 l gs col4 s gr % Polyline n 10500 4125 m 10500 4275 l gs col4 s gr % Polyline n 10425 4500 m 10575 4500 l gs col4 s gr % Polyline n 10500 4425 m 10500 4575 l gs col4 s gr % Polyline n 10425 4800 m 10575 4800 l gs col4 s gr % Polyline n 10500 4725 m 10500 4875 l gs col4 s gr % Polyline n 11625 900 m 11775 900 l gs col4 s gr % Polyline n 11700 825 m 11700 975 l gs col4 s gr % Polyline n 11625 1200 m 11775 1200 l gs col4 s gr % Polyline n 11700 1125 m 11700 1275 l gs col4 s gr % Polyline n 11625 1500 m 11775 1500 l gs col4 s gr % Polyline n 11700 1425 m 11700 1575 l gs col4 s gr % Polyline n 11625 1800 m 11775 1800 l gs col4 s gr % Polyline n 11700 1725 m 11700 1875 l gs col4 s gr % Polyline n 11625 2100 m 11775 2100 l gs col4 s gr % Polyline n 11700 2025 m 11700 2175 l gs col4 s gr % Polyline n 11625 2400 m 11775 2400 l gs col4 s gr % Polyline n 11700 2325 m 11700 2475 l gs col4 s gr % Polyline n 11625 2700 m 11775 2700 l gs col4 s gr % Polyline n 11700 2625 m 11700 2775 l gs col4 s gr % Polyline n 11625 3000 m 11775 3000 l gs col4 s gr % Polyline n 11700 2925 m 11700 3075 l gs col4 s gr % Polyline n 11625 3300 m 11775 3300 l gs col4 s gr % Polyline n 11700 3225 m 11700 3375 l gs col4 s gr % Polyline n 11625 3600 m 11775 3600 l gs col4 s gr % Polyline n 11700 3525 m 11700 3675 l gs col4 s gr % Polyline n 11625 3900 m 11775 3900 l gs col4 s gr % Polyline n 11700 3825 m 11700 3975 l gs col4 s gr % Polyline n 11625 4200 m 11775 4200 l gs col4 s gr % Polyline n 11700 4125 m 11700 4275 l gs col4 s gr % Polyline n 11625 4500 m 11775 4500 l gs col4 s gr % Polyline n 11700 4425 m 11700 4575 l gs col4 s gr % Polyline n 11625 4800 m 11775 4800 l gs col4 s gr % Polyline n 11700 4725 m 11700 4875 l gs col4 s gr % Polyline 7.500 slw n 900 900 m 900 5100 l 12900 5100 l 12900 900 l gs col0 s gr $F2psEnd rs %%EndDocument @endspecial 0 0 0 TeXcolorrgb 2819 173 a Fc(\012)2934 199 y Fg(4)p Black 0 0 0 TeXcolorrgb 982 173 a Fc(\012)1097 199 y Fg(1)p Black 788 1267 a currentpoint currentpoint translate 1 0.38373 div 1 0.38373 div scale neg exch neg exch translate 788 1267 a 515 1449 a FB(Figure)53 b(3:)89 b(The)54 b(b)r(o)n(x)g(\012)g(is)g(obtained)g(b)n(y)f (splitting)i(\003)2486 1461 y Fz(N)2602 1449 y FB(in)n(to)f(strips)f (of)h(width)515 1549 y([)p FA(A\025)648 1519 y Fv(\000)p Fx(2)p Fz(=)p Fx(3)805 1549 y Fy(j)14 b FB(log)g FA(\025)p Fy(j)1034 1519 y Fv(\000)p Fx(2)1123 1549 y FB(])38 b(b)n(y)f(forcing)f (all)h(the)h(spins)f(on)g(the)h(corresp)r(onding)d(v)n(ertical)h(half-) 515 1649 y(lines)27 b(to)h(tak)n(e)f(the)h(v)-5 b(alue)27 b(+1.)p Black 515 1897 a(F)-7 b(rom)27 b(this)h(and)f(a)g(standard)g (large)f(deviations)h(estimate,)h(w)n(e)f(get)g(that)561 2114 y FA(\026)611 2126 y Fv(\006)p Fz(;)p Fx(0)p Fz(;)p Fx(\012)801 1997 y Fw(\022)862 2114 y FB(#)p Fy(f)p FA(k)f FB(:)37 b Fy(j)p FB(\003)1183 2079 y Fv(\000)1183 2139 y Fz(k)1239 2114 y Fy(j)23 b FA(<)f(K)1443 2126 y Fz(\025)1486 2114 y Fy(g)h(\025)1648 2058 y FB(15)p 1648 2095 84 4 v 1648 2171 a(16)2043 2058 y FA(N)p 1765 2095 632 4 v 1765 2173 a FB([)p FA(A\025)1898 2149 y Fv(\000)p Fx(2)p Fz(=)p Fx(3)2055 2173 y Fy(j)14 b FB(log)g FA(\025)p Fy(j)2284 2149 y Fv(\000)p Fx(2)2374 2173 y FB(])2407 1997 y Fw(\023)2491 2114 y Fy(\024)23 b FA(e)2618 2080 y Fv(\000)p Fz(C)t(A)2772 2055 y Fn(\000)p Fm(1)2860 2080 y Fz(\025)2899 2055 y Fm(2)p Fu(=)p Fm(3)3001 2080 y Fv(j)12 b Fx(log)g Fz(\025)p Fv(j)3189 2055 y Fm(2)3233 2080 y Fz(N)3309 2114 y FA(:)515 2346 y FB(\(Notice)41 b(that)h(the)f(ev)n(en)n(ts)g Fy(fj)p FB(\003)1560 2311 y Fv(\000)1560 2371 y Fz(k)1615 2346 y Fy(j)46 b FA(<)f(K)1865 2358 y Fz(\025)1909 2346 y Fy(g)40 b FB(are)h(indep)r(enden)n(t)h (under)f FA(\026)2927 2358 y Fv(\006)p Fz(;)p Fx(0)p Fz(;)p Fx(\012)3103 2346 y FB(\).)78 b(The)515 2446 y(prop)r(osition)32 b(easily)h(follo)n(ws)g(from)g(this,)j(pro)n(vided)c FA(\025)i FB(is)g(c)n(hosen)f(small)g(enough)g(\(for)g(a)515 2545 y(\014xed)27 b(small)h FA(A)p FB(\).)37 b(Indeed,)28 b(on)f(the)h(complemen)n(tary)f(ev)n(en)n(t,)g(i.e.)1156 2760 y(#)p Fy(f)p FA(k)f FB(:)37 b Fy(j)p FB(\003)1477 2725 y Fv(\000)1477 2785 y Fz(k)1532 2760 y Fy(j)24 b FA(>)e(K)1737 2772 y Fz(\025)1780 2760 y Fy(g)h FA(>)1963 2704 y FB(1)p 1942 2741 84 4 v 1942 2817 a(16)2337 2704 y FA(N)p 2059 2741 632 4 v 2059 2819 a FB([)p FA(A\025)2192 2795 y Fv(\000)p Fx(2)p Fz(=)p Fx(3)2349 2819 y Fy(j)14 b FB(log)g FA(\025)p Fy(j)2578 2795 y Fv(\000)p Fx(2)2668 2819 y FB(])2715 2760 y FA(;)515 2978 y FB(w)n(e)27 b(ha)n(v)n(e)1169 3078 y Fy(j)p FB(\003)1250 3044 y Fv(\000)1306 3078 y Fy(j)c FA(>)1466 3045 y Fx(1)p 1450 3059 67 4 v 1450 3107 a(16)1526 3078 y FA(N)r(=)p FB([)p FA(A\025)1770 3044 y Fv(\000)p Fx(2)p Fz(=)p Fx(3)1926 3078 y Fy(j)14 b FB(log)g FA(\025)p Fy(j)2155 3044 y Fv(\000)p Fx(2)2245 3078 y FB(])g FA(K)2353 3090 y Fz(\025)2419 3078 y FA(>)22 b(C)2565 3090 y Fz(\025;N)2702 3078 y FA(;)515 3221 y FB(for)27 b(small)g FA(\025)p FB(.)37 b(Let)28 b(us)g(no)n(w)f(pro)n(v) n(e)f(\(2.8\))o(.)639 3321 y(Denote)33 b(b)n(y)f FA(x)1096 3291 y Fz(l)1155 3321 y FB(and)g FA(x)1368 3291 y Fz(r)1438 3321 y FB(the)h(dual)f(sites)h(whic)n(h)f(are)g(the)g(b)r(ottom)h(left) g(and)g(b)r(ottom)515 3421 y(righ)n(t)38 b(corners)e(of)j(\012)1190 3433 y Fx(1)1266 3421 y FB(\(so)f(these)g(are)g(the)h(endp)r(oin)n(ts)f (of)h(the)g(op)r(en)f(path)h(in)g(\012)3171 3433 y Fx(1)3208 3421 y FB(,)i(see)515 3520 y(Fig.)28 b(4\).)40 b(Let)29 b FA(a)1016 3532 y Fz(l)1066 3520 y FB(=)c FA(x)1203 3490 y Fz(l)1203 3541 y Fx(1)1260 3520 y FB(+)18 b([\()1408 3487 y Fx(1)p 1409 3501 34 4 v 1409 3549 a(2)1471 3520 y Fy(\000)h FA(A)1617 3490 y Fx(2)1654 3520 y Fy(j)14 b FB(log)g FA(\025)p Fy(j)1883 3490 y Fv(\000)p Fx(1)1973 3520 y FB(\))p FA(A\025)2115 3490 y Fv(\000)p Fx(2)p Fz(=)p Fx(3)2272 3520 y Fy(j)g FB(log)g FA(\025)p Fy(j)2501 3490 y Fv(\000)p Fx(2)2591 3520 y FB(])28 b(and)h FA(a)2849 3532 y Fz(r)2910 3520 y FB(=)c FA(x)3047 3532 y Fz(r)3103 3520 y Fy(\000)19 b FB([\()3252 3487 y Fx(1)p 3252 3501 V 3252 3549 a(2)3314 3520 y Fy(\000)515 3631 y FA(A)577 3601 y Fx(2)614 3631 y Fy(j)14 b FB(log)g FA(\025)p Fy(j)843 3601 y Fv(\000)p Fx(1)933 3631 y FB(\))p FA(A\025)1075 3601 y Fv(\000)p Fx(2)p Fz(=)p Fx(3)1232 3631 y Fy(j)g FB(log)g FA(\025)p Fy(j)1461 3601 y Fv(\000)p Fx(2)1551 3631 y FB(].)37 b(W)-7 b(e)28 b(in)n(tro)r(duce)f(the)h(follo)n(wing)e (sets)i(of)f(dual)h(sites:)848 3803 y(\001)917 3815 y Fz(l)966 3803 y FB(=)23 b Fy(f)p FA(x)g Fy(2)g Fq(Z)1299 3769 y Fx(2)p Fz(;)p Fv(\003)1414 3803 y FB(:)37 b FA(x)1521 3815 y Fx(1)1581 3803 y FB(=)23 b FA(a)1713 3815 y Fz(l)1738 3803 y FA(;)1799 3771 y Fx(1)p 1799 3785 V 1799 3832 a(2)1865 3803 y Fy(\024)g FA(x)2000 3815 y Fx(2)2061 3803 y FA(<)f(A\025)2258 3769 y Fv(\000)p Fx(1)p Fz(=)p Fx(3)2415 3803 y Fy(j)14 b FB(log)g FA(\025)p Fy(j)2644 3769 y Fv(\000)p Fx(1)2734 3803 y Fy(g)837 3944 y FB(\001)906 3956 y Fz(r)966 3944 y FB(=)23 b Fy(f)p FA(x)g Fy(2)g Fq(Z)1299 3910 y Fx(2)p Fz(;)p Fv(\003)1414 3944 y FB(:)37 b FA(x)1521 3956 y Fx(1)1581 3944 y FB(=)23 b FA(a)1713 3956 y Fz(r)1750 3944 y FA(;)1810 3912 y Fx(1)p 1810 3926 V 1810 3973 a(2)1876 3944 y Fy(\024)g FA(x)2011 3956 y Fx(2)2072 3944 y FA(<)g(A\025)2270 3910 y Fv(\000)p Fx(1)p Fz(=)p Fx(3)2426 3944 y Fy(j)14 b FB(log)g FA(\025)p Fy(j)2655 3910 y Fv(\000)p Fx(1)2745 3944 y Fy(g)874 4069 y FB(\001)23 b(=)g(\001)1123 4081 y Fz(l)1167 4069 y Fy([)c FB(\001)1310 4081 y Fz(r)876 4210 y FA(B)27 b FB(=)c Fy(f)p FA(x)g Fy(2)g Fq(Z)1299 4175 y Fx(2)p Fz(;)p Fv(\003)1414 4210 y FB(:)37 b FA(a)1518 4222 y Fz(l)1566 4210 y FA(<)23 b(x)1701 4222 y Fx(1)1761 4210 y FA(<)g(a)1893 4222 y Fz(r)1930 4210 y FA(;)1990 4177 y Fx(1)p 1990 4191 V 1990 4238 a(2)2057 4210 y Fy(\024)f FA(x)2191 4222 y Fx(2)2252 4210 y FA(<)2350 4177 y Fx(1)p 2350 4191 V 2350 4238 a(2)2393 4210 y FA(A\025)2503 4175 y Fv(\000)p Fx(1)p Fz(=)p Fx(3)2660 4210 y Fy(j)14 b FB(log)f FA(\025)p Fy(j)2888 4175 y Fv(\000)p Fx(1)2978 4210 y Fy(g)h FA(:)515 4382 y FB(W)-7 b(e)28 b(are)e(going)h(to)g(sho)n (w)g(that)1464 4488 y Fw(X)1396 4680 y Fz(\015)t Fx(:)p Fz(x)1492 4655 y Fu(l)1515 4680 y Fv(!)p Fz(x)1619 4655 y Fu(r)1413 4744 y Fz(\015)t Fv(\\)p Fz(B)s Fx(=)p Fv(;)1666 4567 y FA(q)1703 4579 y Fx(\012)1750 4587 y Fm(1)1787 4567 y FB(\()p FA(\015)5 b FB(\))23 b Fy(\025)2020 4534 y Fx(1)p 2020 4548 V 2020 4595 a(8)2077 4567 y Fy(h)p FA(\033)2156 4584 y Fz(x)2194 4567 y Fu(l)8 b FA(\033)2269 4579 y Fz(x)2307 4563 y Fu(r)2345 4567 y Fy(i)2377 4579 y Fx(\012)2424 4587 y Fm(1)2475 4567 y FA(;)710 b FB(\(2.9\))515 4907 y(whic)n(h)23 b(readily)g(implies)g(\(2.8\))h(since)f Fy(j)p FA(B)t Fy(j)g FA(>)g(K)1985 4919 y Fz(\025)2052 4907 y FB(\(when)h FA(\025)g FB(is)f(small\).)35 b(T)-7 b(o)23 b(pro)n(v)n(e)f(\(2.9\),)i(w)n(e)515 5006 y(\014rst)i(sho)n(w)g (that)h(the)g(op)r(en)g(con)n(tour)e(t)n(ypically)h(do)r(es)h(not)f (hit)i(\001.)36 b(This)27 b(is)g(equiv)-5 b(alen)n(t)26 b(to)p Black Black eop end %%Page: 22 22 TeXDict begin 22 21 bop Black 515 232 a Fr(En)n(tropic)22 b(repulsion)g(in)f(external)h(\014eld;)g(v)n(ersion)f(from)g(July)g(3,) f(2003)1118 b FB(22)p Black 515 523 a(sa)n(ying)24 b(that)j(\003)1004 488 y Fv(\000)1004 545 y Fx(1)1086 523 y FB(con)n(tains)e(the)h(set)g (\001.)37 b(But)26 b(this)g(is)g(a)g(decreasing)f(ev)n(en)n(t.)35 b(Therefore,)26 b(if)515 623 y(w)n(e)h(in)n(tro)r(duce)g(the)h(new)g(b) r(o)n(x)1276 781 y Fw(e)1269 802 y FB(\012)1329 814 y Fx(1)1389 802 y FB(=)23 b Fy(f)p FA(x)g FB(=)g(\()p FA(x)1756 814 y Fx(1)1794 802 y FA(;)14 b(x)1878 814 y Fx(2)1915 802 y FB(\))24 b(:)37 b(\()p FA(x)2110 814 y Fx(1)2148 802 y FA(;)14 b Fy(j)p FA(x)2255 814 y Fx(2)2292 802 y Fy(j)p FB(\))24 b Fy(2)f FB(\012)2509 814 y Fx(1)2546 802 y Fy(g)14 b FA(;)515 980 y FB(and)27 b(the)h(new)g(set)1309 1059 y Fw(e)1297 1080 y FB(\001)23 b(=)g Fy(f)p FA(x)g FB(=)g(\()p FA(x)1756 1092 y Fx(1)1794 1080 y FA(;)14 b(x)1878 1092 y Fx(2)1915 1080 y FB(\))24 b(:)37 b(\()p FA(x)2110 1092 y Fx(1)2148 1080 y FA(;)14 b Fy(j)p FA(x)2255 1092 y Fx(2)2292 1080 y Fy(j)p FB(\))24 b Fy(2)f FB(\001)p Fy(g)14 b FA(;)515 1227 y FB(then)28 b(b)n(y)f(FK)n(G)g(inequalities,) 893 1406 y FA(\026)943 1418 y Fv(\006)p Fz(;)p Fx(0)p Fz(;)p Fx(\012)1115 1426 y Fm(1)1151 1406 y FB(\(\003)1241 1371 y Fv(\000)1241 1428 y Fx(1)1320 1406 y Fy(\033)c FB(\001\))h Fy(\025)e FA(\026)1670 1434 y Fv(\006)p Fz(;)p Fx(0)p Fz(;)1800 1419 y Fk(e)1795 1434 y Fx(\012)1842 1442 y Fm(1)1879 1406 y FB(\(\003)1969 1371 y Fv(\000)1969 1428 y Fx(1)2048 1406 y Fy(\033)g FB(\001\))i Fy(\025)e FA(\026)2397 1434 y Fv(\006)p Fz(;)p Fx(0)p Fz(;)2527 1419 y Fk(e)2522 1434 y Fx(\012)2569 1442 y Fm(1)2606 1406 y FB(\(\003)2696 1371 y Fv(\000)2696 1428 y Fx(1)2775 1406 y Fy(\033)2874 1385 y Fw(e)2862 1406 y FB(\001)q(\))14 b FA(:)515 1585 y FB(The)27 b(latter)g(probabilit)n(y)f(is)h(easily)f (b)r(ounded.)37 b(Indeed,)28 b(b)n(y)f(symmetry)f(it)i(is)f(larger)e (than)1440 1743 y Fx(1)p 1440 1757 34 4 v 1440 1805 a(2)1497 1776 y Fy(h)p FA(\033)1576 1793 y Fz(x)1614 1776 y Fu(l)9 b FA(\033)1690 1788 y Fz(x)1728 1772 y Fu(r)1765 1776 y Fy(i)1797 1741 y Fv(\000)p Fx(1)1802 1802 y Fk(e)1797 1817 y Fx(\012)1844 1825 y Fm(1)1992 1697 y Fw(X)1924 1889 y Fz(\015)t Fx(:)p Fz(x)2020 1864 y Fu(l)2042 1889 y Fv(!)p Fz(x)2146 1864 y Fu(r)1940 1966 y Fz(\015)t Fv(\\)2032 1951 y Fk(e)2024 1966 y Fx(\001)o(=)p Fv(;)2194 1776 y FA(q)2236 1789 y Fk(e)2231 1804 y Fx(\012)2278 1812 y Fm(1)2315 1776 y FB(\()p FA(\015)c FB(\))p FA(;)515 2135 y FB(and)27 b(the)h(latter)f(expression)g(is)g(larger)f(than)h(1)p FA(=)p FB(4)g(since)1187 2252 y Fw(X)1119 2444 y Fz(\015)t Fx(:)p Fz(x)1215 2419 y Fu(l)1238 2444 y Fv(!)p Fz(x)1342 2419 y Fu(r)1136 2521 y Fz(\015)t Fv(\\)1228 2506 y Fk(e)1220 2521 y Fx(\001)o Fv(6)p Fx(=)p Fv(;)1389 2331 y FA(q)1431 2344 y Fk(e)1426 2359 y Fx(\012)1473 2367 y Fm(1)1510 2331 y FB(\()p FA(\015)5 b FB(\))24 b Fy(\024)1743 2252 y Fw(X)1733 2447 y Fz(u)p Fv(2)1825 2432 y Fk(e)1817 2447 y Fx(\001)1872 2331 y Fy(h)p FA(\033)1951 2348 y Fz(x)1989 2331 y Fu(l)8 b FA(\033)2064 2343 y Fz(u)2108 2331 y Fy(i)2145 2344 y Fk(e)2140 2359 y Fx(\012)2187 2367 y Fm(1)2238 2331 y Fy(h)p FA(\033)2317 2343 y Fz(u)2361 2331 y FA(\033)2408 2343 y Fz(x)2446 2327 y Fu(r)2484 2331 y Fy(i)2521 2344 y Fk(e)2516 2359 y Fx(\012)2563 2367 y Fm(1)1646 2714 y Fy(\024)22 b FA(C)1835 2635 y Fw(X)1826 2830 y Fz(u)p Fv(2)1918 2815 y Fk(e)1910 2830 y Fx(\001)2006 2657 y FA(e)2045 2627 y Fv(\000)p Fz(\034)7 b Fx(\()p Fz(u)p Fv(\000)p Fz(x)2290 2602 y Fu(l)2313 2627 y Fx(\))p 1989 2695 373 4 v 1989 2772 a Fy(j)p FA(u)18 b Fy(\000)g FA(x)2208 2784 y Fz(l)2233 2772 y Fy(j)2256 2748 y Fx(1)p Fz(=)p Fx(2)2400 2657 y FA(e)2439 2627 y Fv(\000)p Fz(\034)7 b Fx(\()p Fz(x)2593 2602 y Fu(r)2625 2627 y Fv(\000)p Fz(u)p Fx(\))p 2381 2695 384 4 v 2381 2772 a Fy(j)p FA(x)2451 2784 y Fz(r)2507 2772 y Fy(\000)18 b FA(u)p Fy(j)2661 2748 y Fx(1)p Fz(=)p Fx(2)1646 3016 y Fy(\024)k FB(3)p FA(C)1884 2960 y(e)1923 2930 y Fv(\000)p Fz(\034)7 b Fx(\()p Fz(x)2077 2905 y Fu(r)2109 2930 y Fv(\000)p Fz(x)2199 2905 y Fu(l)2223 2930 y Fx(\))p 1864 2997 410 4 v 1864 3074 a Fy(j)p FA(x)1934 3086 y Fz(r)1990 3074 y Fy(\000)18 b FA(x)2120 3086 y Fz(l)2145 3074 y Fy(j)2168 3050 y Fx(1)p Fz(=)p Fx(2)2463 2960 y Fy(j)2498 2939 y Fw(e)2486 2960 y FB(\001)p Fy(j)p 2316 2997 V 2316 3074 a(j)p FA(x)2386 3086 y Fz(r)2442 3074 y Fy(\000)g FA(x)2572 3086 y Fz(l)2598 3074 y Fy(j)2621 3050 y Fx(1)p Fz(=)p Fx(2)1646 3198 y Fy(\024)1743 3166 y Fx(1)p 1743 3180 34 4 v 1743 3227 a(2)1800 3198 y Fy(h)p FA(\033)1879 3215 y Fz(x)1917 3199 y Fu(l)1946 3198 y FA(\033)1993 3210 y Fz(x)2031 3194 y Fu(r)2068 3198 y Fy(i)2105 3211 y Fk(e)2100 3226 y Fx(\012)2147 3234 y Fm(1)2198 3198 y FA(;)515 3377 y FB(pro)n(vided)26 b FA(A)i FB(is)g(c)n(hosen)e(small) i(enough.)36 b(W)-7 b(e)28 b(ha)n(v)n(e)e(th)n(us)i(sho)n(wn)f(that) 1503 3556 y FA(\026)1553 3568 y Fv(\006)p Fz(;)p Fx(0)p Fz(;)p Fx(\012)1725 3576 y Fm(1)1761 3556 y FB(\(\003)1851 3521 y Fv(\000)1851 3578 y Fx(1)1930 3556 y Fy(\033)c FB(\001\))g Fy(\025)g FB(1)p FA(=)p FB(4)14 b FA(:)774 b FB(\(2.10\))639 3735 y(W)-7 b(e)26 b(no)n(w)f(restrict)f(our)h(atten) n(tion)g(to)g(op)r(en)g(paths)h FA(\015)j FB(in)d(\012)2485 3747 y Fx(1)2548 3735 y FB(not)f(in)n(tersecting)f(\001,)i(but)515 3835 y(in)n(tersecting)h FA(B)t FB(.)40 b(T)-7 b(o)28 b(eac)n(h)g(suc)n(h)g(paths)g(w)n(e)g(asso)r(ciate)f(three)h(dual)h (sites:)38 b(the)29 b(\014rst)f(visit)515 3934 y(to)j(the)g(set)g Fy(f)p FA(x)e FB(:)43 b FA(x)1130 3946 y Fx(1)1196 3934 y FB(=)29 b FA(a)1334 3946 y Fz(l)1359 3934 y FA(;)f(x)h Fy(62)h FB(\001)1640 3946 y Fz(l)1665 3934 y Fy(g)p FB(,)i(the)f(last)g (visit)g(to)g Fy(f)p FA(x)e FB(:)43 b FA(x)2591 3946 y Fx(1)2657 3934 y FB(=)29 b FA(a)2795 3946 y Fz(r)2831 3934 y FA(;)f(x)h Fy(62)h FB(\001)3112 3946 y Fz(r)3149 3934 y Fy(g)p FB(,)h(and)515 4034 y(the)i(\014rst)f(visit)h(to)g FA(B)t FB(.)53 b(W)-7 b(e)33 b(denote)f(these)h(dual)g(sites)g(b)n(y)f FA(b)2452 4004 y Fz(l)2477 4034 y FB(,)i FA(b)2570 4004 y Fz(r)2640 4034 y FB(and)e FA(b)2842 4004 y Fz(m)2938 4034 y FB(resp)r(ectiv)n(ely)-7 b(.)515 4134 y(Using)28 b(\(A.16\),)g(w)n(e)f(then)h(ha)n(v)n(e)784 4250 y Fw(X)715 4443 y Fz(\015)t Fx(:)p Fz(x)811 4418 y Fu(l)834 4443 y Fv(!)p Fz(x)938 4418 y Fu(r)732 4506 y Fz(\015)t Fv(\\)p Fx(\001=)p Fv(;)733 4569 y Fz(\015)t Fv(\\)p Fz(B)s Fv(6)p Fx(=)p Fv(;)985 4329 y FA(q)1022 4341 y Fx(\012)1069 4349 y Fm(1)1106 4329 y FB(\()p FA(\015)5 b FB(\))24 b Fy(\024)1389 4250 y Fw(X)1329 4434 y Fz(b)1358 4418 y Fu(l)1383 4434 y Fz(;b)1432 4418 y Fu(m)1487 4434 y Fz(;b)1536 4418 y Fu(r)1569 4329 y Fy(h)p FA(\033)1648 4346 y Fz(x)1686 4329 y Fu(l)9 b FA(\033)1762 4346 y Fz(b)1791 4329 y Fu(l)g Fy(i)1852 4341 y Fx(\012)1899 4349 y Fm(1)1959 4329 y Fy(h)p FA(\033)2038 4346 y Fz(b)2067 4329 y Fu(l)g FA(\033)2143 4341 y Fz(b)2172 4325 y Fu(m)2232 4329 y Fy(i)2264 4341 y Fx(\012)2311 4349 y Fm(1)2371 4329 y Fy(h)p FA(\033)2450 4341 y Fz(b)2479 4325 y Fu(m)2539 4329 y FA(\033)2586 4341 y Fz(b)2615 4325 y Fu(r)2654 4329 y Fy(i)2686 4341 y Fx(\012)2733 4349 y Fm(1)2793 4329 y Fy(h)p FA(\033)2872 4341 y Fz(b)2901 4325 y Fu(r)2939 4329 y FA(\033)2986 4341 y Fz(x)3024 4325 y Fu(r)3062 4329 y Fy(i)3094 4341 y Fx(\012)3141 4349 y Fm(1)515 4734 y FB(W)-7 b(e)28 b(\014rst)f(observ)n(e)f(that)1236 4834 y Fw(X)1139 5021 y Fz(b)1168 5005 y Fu(l)1192 5021 y Fx(:)11 b Fz(b)1251 5001 y Fu(l)1251 5039 y Fm(2)1284 5021 y Fz(>\025)1375 5005 y Fn(\000)p Fm(1)1452 4913 y Fy(h)p FA(\033)1531 4930 y Fz(x)1569 4913 y Fu(l)e FA(\033)1645 4930 y Fz(b)1674 4913 y Fu(l)g Fy(i)1735 4925 y Fx(\012)1782 4933 y Fm(1)1842 4913 y Fy(\024)23 b FA(e)1969 4879 y Fv(\000)p Fz(C)14 b(\025)2122 4854 y Fn(\000)p Fm(1)2227 4913 y Fy(\034)23 b(h)p FA(\033)2412 4930 y Fz(x)2450 4913 y Fu(l)9 b FA(\033)2526 4925 y Fz(x)2564 4909 y Fu(r)2602 4913 y Fy(i)2634 4925 y Fx(\012)2681 4933 y Fm(1)2732 4913 y FA(;)p Black Black eop end %%Page: 23 23 TeXDict begin 23 22 bop Black 515 232 a Fr(En)n(tropic)22 b(repulsion)g(in)f(external)h(\014eld;)g(v)n(ersion)f(from)g(July)g(3,) f(2003)1118 b FB(23)p Black Black 1000 1621 a currentpoint currentpoint translate 0.30696 0.30696 scale neg exch neg exch translate 1000 1621 a @beginspecial 0 @llx 0 @lly 737 @urx 462 @ury 7370 @rwi @setspecial %%BeginDocument: minvol.pstex %!PS-Adobe-2.0 EPSF-2.0 %%Title: minvol.pstex %%Creator: fig2dev Version 3.2 Patchlevel 3d %%CreationDate: Mon Jul 1 11:09:04 2002 %%For: velenik@eupalidos.cmi.univ-mrs.fr (Yvan VELENIK, CR probabilites) %%BoundingBox: 0 0 737 462 %%Magnification: 1.0000 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save newpath 0 462 moveto 0 0 lineto 737 0 lineto 737 462 lineto closepath clip newpath -22.5 605.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def $F2psBegin 10 setmiterlimit 0.06000 0.06000 sc % % Fig objects follow % % Polyline n 5400 7500 m 7800 7500 l 7800 9600 l 5400 9600 l cp gs col2 0.50 tnt ef gr % Polyline 7.500 slw n 600 2400 m 600 9600 l 12600 9600 l 12600 2400 l gs col0 s gr % Polyline [60] 0 sd n 7800 5400 m 7800 2400 l gs col0 s gr [] 0 sd % Polyline [60] 0 sd n 5400 5400 m 5400 2400 l gs col0 s gr [] 0 sd % Polyline 30.000 slw n 5400 9600 m 5400 5400 l gs col14 s gr % Polyline n 7800 9600 m 7800 5400 l gs col14 s gr % Polyline 7.500 slw n 600 9600 m 1050 9600 l 1050 9150 l 825 9150 l 825 8775 l 1425 8775 l 1425 8925 l 1350 8925 l 1350 9150 l 1725 9150 l 1725 8475 l 2550 8475 l 2550 8625 l 3150 8625 l 3150 8850 l 3375 8850 l 3375 8100 l 2625 8100 l 2625 7950 l 3150 7950 l 3150 7725 l 2775 7725 l 2775 6825 l 3000 6825 l 3000 7200 l 3150 7200 l 3150 6825 l 3900 6825 l 3900 6675 l 3600 6675 l 3600 6450 l 3225 6450 l 3225 5925 l 2700 5925 l 2700 5775 l 2400 5775 l 2400 5625 l 3000 5625 l 3000 5400 l 3525 5400 l 3525 5175 l 3900 5175 l 3900 5325 l 4575 5325 l 4575 5025 l 4200 5025 l 4200 4725 l 4650 4725 l 4650 4500 l 3975 4500 l 3975 4350 l 4875 4350 l 4875 4125 l 5175 4125 l 5175 3900 l 5700 3900 l 5700 3750 l 5250 3750 l 5250 3600 l 6000 3600 l 6000 4050 l 6450 4050 l 6450 3975 l 6225 3975 l 6225 3825 l 6675 3825 l 6675 4425 l 6225 4425 l 6225 4650 l 6675 4650 l 6675 4950 l 6075 4950 l 6075 5625 l 5925 5625 l 5925 6225 l 6150 6225 l 6150 6900 l 5925 6900 l 5925 7350 l 6150 7350 l 6150 7875 l 6750 7875 l 6750 7650 l 6450 7650 l 6450 7425 l 7050 7425 l 7050 8025 l 6825 8025 l 6825 8175 l 7275 8175 l 7275 7200 l 6750 7200 l 6750 6975 l 6450 6975 l 6450 6225 l 6525 6225 l 6525 5250 l 6975 5250 l 6975 4875 l 7350 4875 l 8025 4875 l 8025 5100 l 7275 5100 l 7275 5250 l 8100 5250 l 8100 5625 l 8475 5625 l 8475 5475 l 9000 5475 l 9000 5625 l 8700 5625 l 8700 5850 l 9375 5850 l 9375 5325 l 9525 5325 l 9525 4875 l 9975 4875 l 9975 5250 l 10200 5250 l 10200 5475 l 9825 5475 l 9825 5550 l 10050 5550 l 10050 5625 l 10575 5625 l 10575 5850 l 11025 5850 l 11025 6225 l 10575 6225 l 10575 6525 l 10350 6525 l 10350 6975 l 10500 6975 l 10500 6675 l 11025 6675 l 11025 7200 l 11550 7200 l 11550 7050 l 11250 7050 l 11250 6900 l 11850 6900 l 11850 7425 l 11550 7425 l 11550 7800 l 11250 7800 l 11250 8025 l 11925 8025 l 11925 8250 l 11700 8250 l 11700 8550 l 11100 8550 l 11100 8700 l 11550 8700 l 11550 8850 l 12225 8850 l 12225 9000 l 12000 9000 l 12000 9225 l 12375 9225 l 12375 9450 l 12525 9450 l 12525 9600 l 12600 9600 l gs col1 s gr % Ellipse n 5400 3900 50 50 0 360 DrawEllipse gs -0.00 setgray ef gr gs col0 s gr % Ellipse n 7800 5250 50 50 0 360 DrawEllipse gs -0.00 setgray ef gr gs col0 s gr % Ellipse n 6150 7500 50 50 0 360 DrawEllipse gs -0.00 setgray ef gr gs col0 s gr % Ellipse n 600 9600 50 50 0 360 DrawEllipse gs -0.00 setgray ef gr gs col0 s gr % Ellipse n 12600 9600 50 50 0 360 DrawEllipse gs -0.00 setgray ef gr gs col0 s gr $F2psEnd rs %%EndDocument @endspecial 0 0 0 TeXcolorrgb -54 x Fb(x)1115 1639 y(l)p Black 0 0 0 TeXcolorrgb 4000 1042 a(B)p Black 0 0 0 TeXcolorrgb 7038 1567 a(x)7153 1639 y(l)p Black 0 0 0 TeXcolorrgb 1900 -645 a(\015)p Black 0 0 0 TeXcolorrgb 4488 -570 a(b)4574 -645 y(r)p Black 0 0 0 TeXcolorrgb 3588 517 a(b)3674 442 y(m)p Black 0 0 0 TeXcolorrgb 4750 -158 a Fa(\001)4909 -127 y Fb(r)p Black 0 0 0 TeXcolorrgb 3550 -1208 a(b)3636 -1283 y(l)p Black 0 0 0 TeXcolorrgb 3213 -158 a Fa(\001)3372 -86 y Fb(l)p Black 1000 1621 a currentpoint currentpoint translate 1 0.30696 div 1 0.30696 div scale neg exch neg exch translate 1000 1621 a Black 1136 1804 a FB(Figure)27 b(4:)37 b(The)27 b(settings)h(for)f(the)h(pro)r(of)f(of)34 b(\(2.8\))o(.)p Black Black 515 2074 a(and)28 b(similarly)h(for)f FA(b)1183 2043 y Fz(r)1219 2074 y FB(,)i(so)e(that)h(w)n(e)g(can)f(restrict)g (the)i(sum)f(o)n(v)n(er)e(these)i(p)r(oin)n(ts)g(to)f(those)515 2173 y(with)33 b(second)f(comp)r(onen)n(t)h(smaller)f(than)h FA(\025)1951 2143 y Fv(\000)p Fx(1)2041 2173 y FB(.)53 b(W)-7 b(e)33 b(no)n(w)f(use)h(the)g(sharp)f(triangle)g(in-)515 2273 y(equalit)n(y)c(\(A.25\))f(to)h(get)622 2455 y FA(\034)9 b FB(\()p FA(b)735 2421 y Fz(m)817 2455 y Fy(\000)18 b FA(b)936 2421 y Fz(l)961 2455 y FB(\))h(+)f FA(\034)9 b FB(\()p FA(b)1208 2421 y Fz(r)1264 2455 y Fy(\000)18 b FA(b)1383 2421 y Fz(m)1446 2455 y FB(\))23 b Fy(\025)g FA(\034)9 b FB(\()p FA(b)1702 2421 y Fz(r)1757 2455 y Fy(\000)18 b FA(b)1876 2421 y Fz(l)1902 2455 y FB(\))g(+)g FA(\024)c FB(\()p Fy(j)p FA(b)2188 2421 y Fz(m)2269 2455 y Fy(\000)k FA(b)2388 2421 y Fz(l)2414 2455 y Fy(j)g FB(+)g Fy(j)p FA(b)2597 2421 y Fz(r)2652 2455 y Fy(\000)g FA(b)2771 2421 y Fz(m)2834 2455 y Fy(j)g(\000)g(j)p FA(b)3017 2421 y Fz(r)3072 2455 y Fy(\000)g FA(b)3191 2421 y Fz(l)3216 2455 y Fy(j)p FB(\))1501 2593 y Fy(\025)23 b FA(\034)9 b FB(\()p FA(b)1702 2559 y Fz(r)1757 2593 y Fy(\000)18 b FA(b)1876 2559 y Fz(l)1902 2593 y FB(\))g(+)g FA(C)6 b(A)2162 2559 y Fv(\000)p Fx(1)2266 2593 y Fy(j)14 b FB(log)g FA(\025)p Fy(j)g FA(;)515 2776 y FB(and)27 b(therefore,)g (using)h(\(A.24\),)938 2958 y Fy(h)p FA(\033)1017 2975 y Fz(b)1046 2959 y Fu(l)1075 2958 y FA(\033)1122 2970 y Fz(b)1151 2954 y Fu(m)1211 2958 y Fy(i)1243 2970 y Fx(\012)1290 2978 y Fm(1)1350 2958 y Fy(h)p FA(\033)1429 2970 y Fz(b)1458 2954 y Fu(m)1518 2958 y FA(\033)1565 2970 y Fz(b)1594 2954 y Fu(r)1633 2958 y Fy(i)1665 2970 y Fx(\012)1712 2978 y Fm(1)1772 2958 y Fy(\024)22 b(h)p FA(\033)1938 2975 y Fz(b)1967 2959 y Fu(l)1997 2958 y FA(\033)2044 2970 y Fz(b)2073 2954 y Fu(m)2133 2958 y Fy(i)h(h)p FA(\033)2267 2970 y Fz(b)2296 2954 y Fu(m)2356 2958 y FA(\033)2403 2970 y Fz(b)2432 2954 y Fu(r)2470 2958 y Fy(i)1772 3109 y(\024)f FA(e)1898 3074 y Fv(\000)p Fz(C)2002 3049 y Fn(0)2024 3074 y Fz(A)2074 3049 y Fn(\000)p Fm(1)2163 3074 y Fv(j)11 b Fx(log)h Fz(\025)p Fv(j)2377 3109 y Fy(h)p FA(\033)2456 3125 y Fz(b)2485 3109 y Fu(l)e FA(\033)2562 3121 y Fz(b)2591 3104 y Fu(r)2629 3109 y Fy(i)k(j)p FA(b)2734 3074 y Fz(r)2789 3109 y Fy(\000)k FA(b)2908 3074 y Fz(l)2933 3109 y Fy(j)1772 3259 y(\024)k FA(e)1898 3224 y Fv(\000)p Fz(C)2002 3199 y Fn(00)2042 3224 y Fz(A)2092 3199 y Fn(\000)p Fm(1)2181 3224 y Fv(j)11 b Fx(log)h Fz(\025)p Fv(j)2396 3259 y Fy(h)p FA(\033)2475 3276 y Fz(b)2504 3259 y Fu(l)d FA(\033)2580 3271 y Fz(b)2609 3255 y Fu(r)2647 3259 y Fy(i)2679 3271 y Fx(\012)2726 3279 y Fm(1)2777 3259 y FA(:)515 3441 y FB(Using)27 b(this)h(and)1098 3624 y Fy(h)p FA(\033)1177 3641 y Fz(x)1215 3624 y Fu(l)8 b FA(\033)1290 3641 y Fz(b)1319 3624 y Fu(l)h Fy(i)1380 3636 y Fx(\012)1427 3644 y Fm(1)1488 3624 y Fy(h)p FA(\033)1567 3641 y Fz(b)1596 3624 y Fu(l)g FA(\033)1672 3636 y Fz(b)1701 3620 y Fu(r)1739 3624 y Fy(i)1771 3636 y Fx(\012)1818 3644 y Fm(1)1878 3624 y Fy(h)p FA(\033)1957 3636 y Fz(b)1986 3620 y Fu(r)2025 3624 y FA(\033)2072 3636 y Fz(x)2110 3620 y Fu(r)2148 3624 y Fy(i)2180 3636 y Fx(\012)2227 3644 y Fm(1)2287 3624 y Fy(\024)22 b(h)p FA(\033)2453 3641 y Fz(x)2491 3624 y Fu(l)9 b FA(\033)2567 3636 y Fz(x)2605 3620 y Fu(r)2643 3624 y Fy(i)2675 3636 y Fx(\012)2722 3644 y Fm(1)2773 3624 y FA(;)515 3807 y FB(whic)n(h)27 b(follo)n(ws)g(from)g(GKS)h(inequalities,)f(w)n(e)g(\014nally)h(get)939 3922 y Fw(X)871 4115 y Fz(\015)t Fx(:)p Fz(x)967 4090 y Fu(l)990 4115 y Fv(!)p Fz(x)1094 4090 y Fu(r)888 4178 y Fz(\015)t Fv(\\)p Fx(\001=)p Fv(;)888 4241 y Fz(\015)t Fv(\\)p Fz(B)s Fv(6)p Fx(=)p Fv(;)1141 4001 y FA(q)1178 4013 y Fx(\012)1225 4021 y Fm(1)1262 4001 y FB(\()p FA(\015)5 b FB(\))23 b Fy(\024)g FA(e)1524 3967 y Fv(\000)p Fz(C)1628 3942 y Fn(000)1686 3967 y Fz(A)1736 3942 y Fn(\000)p Fm(1)1825 3967 y Fv(j)11 b Fx(log)h Fz(\025)p Fv(j)2039 4001 y Fy(h)p FA(\033)2118 4018 y Fz(x)2156 4002 y Fu(l)2185 4001 y FA(\033)2232 4013 y Fz(x)2270 3997 y Fu(r)2308 4001 y Fy(i)2340 4013 y Fx(\012)2387 4021 y Fm(1)2447 4001 y Fy(\024)2545 3969 y Fx(1)p 2545 3983 34 4 v 2545 4030 a(8)2601 4001 y Fy(h)p FA(\033)2680 4018 y Fz(x)2718 4002 y Fu(l)2747 4001 y FA(\033)2794 4013 y Fz(x)2832 3997 y Fu(r)2870 4001 y Fy(i)2902 4013 y Fx(\012)2949 4021 y Fm(1)3000 4001 y FA(:)515 4415 y FB(W)-7 b(e)28 b(deduce)f(from)h(the)g(latter)f(b)r(ound)h(and)f(\(2.10\))g(that)1354 4535 y Fw(X)1286 4727 y Fz(\015)t Fx(:)p Fz(x)1382 4702 y Fu(l)1405 4727 y Fv(!)p Fz(x)1509 4702 y Fu(r)1304 4791 y Fz(\015)t Fv(\\)p Fz(B)s Fv(6)p Fx(=)p Fv(;)1556 4614 y FA(q)1593 4626 y Fx(\012)1640 4634 y Fm(1)1677 4614 y FB(\()p FA(\015)5 b FB(\))24 b Fy(\024)e FB(\()1942 4581 y Fx(1)p 1942 4595 V 1942 4642 a(8)2004 4614 y FB(+)2097 4581 y Fx(3)p 2097 4595 V 2097 4642 a(4)2140 4614 y FB(\))14 b Fy(h)p FA(\033)2265 4631 y Fz(x)2303 4614 y Fu(l)9 b FA(\033)2379 4626 y Fz(x)2417 4610 y Fu(r)2454 4614 y Fy(i)2486 4626 y Fx(\012)2533 4634 y Fm(1)2584 4614 y FA(;)515 4964 y FB(and)27 b(\(2.9\))g(is)h(pro)n(v)n(ed.)p Black Black eop end %%Page: 24 24 TeXDict begin 24 23 bop Black 515 232 a Fr(En)n(tropic)22 b(repulsion)g(in)f(external)h(\014eld;)g(v)n(ersion)f(from)g(July)g(3,) f(2003)1118 b FB(24)p Black 515 523 a Fp(2.3.3)93 b(Pro)s(of)32 b(of)g(the)g(upp)s(er)f(b)s(ound)515 676 y FB(Let)i(us)g(write)g FA(V)51 b FB(=)31 b FA(K)6 b Fy(j)14 b FB(log)g FA(\025)p Fy(j)1500 646 y Fx(2)1538 676 y FA(\025)1586 646 y Fv(\000)p Fx(1)p Fz(=)p Fx(3)1742 676 y FA(N)9 b FB(,)35 b(where)d FA(K)39 b FB(will)33 b(b)r(e)g(c)n(hosen)f(su\016cien)n(tly)h(large)515 776 y(later)27 b(on.)36 b(W)-7 b(e)28 b(w)n(an)n(t)f(to)h(b)r(ound)g (from)f(ab)r(o)n(v)n(e)f(the)i(follo)n(wing)f(probabilit)n(y:)1505 953 y FA(\026)1555 965 y Fv(\006)p Fz(;\025;)p Fx(\003)1731 973 y Fu(N)1802 885 y Fw(\000)1840 953 y Fy(j)p FA(C)1928 918 y Fv(\000)1984 953 y FB(\()14 b Fy(\001)g FB(\))p Fy(j)24 b(\025)f FA(V)2300 885 y Fw(\001)2366 953 y FA(;)515 1129 y FB(where)i FA(C)818 1099 y Fv(\000)875 1129 y FB(\()p FA(\033)s FB(\))i(is)f(the)g(set)g(of)g(all)g(sites)g(in)g (\003)1911 1141 y Fz(N)2000 1129 y FB(that)g(are)f(connected)h(to)g (the)g(b)r(ottom)h(w)n(all)515 1229 y(b)n(y)e(a)g(path)g(of)h Fy(\000)f FB(spins)g(in)h FA(\033)s FB(.)36 b(Our)25 b(aim)g(is)h(to)f(sho)n(w)g(that)g(this)h(probabilit)n(y)e(go)r(es)h (to)g(zero)515 1329 y(with)j FA(N)9 b FB(,)27 b(pro)n(vided)g FA(K)33 b FB(has)27 b(b)r(een)h(c)n(hosen)f(large)f(enough.)639 1428 y(W)-7 b(e)28 b(start)f(with)h(the)g(follo)n(wing)f(ob)n(vious)f (upp)r(er)i(b)r(ound:)891 1596 y FA(Z)948 1608 y Fv(\006)p Fz(;\025;)p Fx(\003)1124 1616 y Fu(N)1195 1596 y FB(\()p Fy(j)p FA(C)1315 1566 y Fv(\000)1371 1596 y FB(\()14 b Fy(\001)g FB(\))p Fy(j)24 b(\025)e FA(V)d FB(\))p 891 1633 830 4 v 1160 1709 a FA(Z)1217 1721 y Fv(\006)p Fz(;\025;)p Fx(\003)1393 1729 y Fu(N)1753 1652 y Fy(\024)1850 1596 y FA(Z)1907 1608 y Fv(\006)p Fz(;\025;)p Fx(\003)2083 1616 y Fu(N)2154 1596 y FB(\()q Fy(j)p FA(C)2275 1566 y Fv(\000)2331 1596 y FB(\()14 b Fy(\001)g FB(\))p Fy(j)23 b(\025)g FA(V)c FB(\))p 1850 1633 V 1853 1709 a FA(Z)1910 1721 y Fv(\006)p Fz(;)p Fx(0)p Fz(;)p Fx(\003)2080 1729 y Fu(N)2151 1709 y FB(\()p Fy(j)p FA(C)2271 1685 y Fv(\000)2328 1709 y FB(\()14 b Fy(\001)g FB(\))p Fy(j)23 b(\025)g FA(V)c FB(\))2716 1596 y FA(Z)2773 1608 y Fv(\006)p Fz(;)p Fx(0)p Fz(;)p Fx(\003)2943 1616 y Fu(N)p 2713 1633 291 4 v 2713 1709 a FA(Z)2770 1721 y Fv(\006)p Fz(;\025;)p Fx(\003)2946 1729 y Fu(N)515 1875 y FB(By)27 b(Lemma)g(3,)1325 1956 y FA(Z)1382 1968 y Fv(\006)p Fz(;)p Fx(0)p Fz(;)p Fx(\003)1552 1976 y Fu(N)p 1321 1993 V 1321 2069 a FA(Z)1378 2081 y Fv(\006)p Fz(;\025;)p Fx(\003)1554 2089 y Fu(N)1645 2012 y Fy(\024)22 b FA(e)1771 1978 y Fz(C)t Fv(j)11 b Fx(log)h Fz(\025)p Fv(j)2010 1953 y Fm(2)2043 1978 y Fz(\025)2082 1953 y Fm(2)p Fu(=)p Fm(3)2173 1978 y Fz(N)2249 1956 y FA(Z)2306 1968 y Fx(+)p Fz(;)p Fx(0)p Fz(;)p Fx(\003)2475 1976 y Fu(N)p 2246 1993 290 4 v 2246 2069 a FA(Z)2303 2081 y Fx(+)p Fz(;\025;)p Fx(\003)2478 2089 y Fu(N)2559 2012 y FA(:)515 2205 y FB(No)n(w)27 b(observ)n(e)f(that)i(w)n(e)f(can)g (write)1117 2380 y FA(Z)1174 2392 y Fx(+)p Fz(;)p Fx(0)p Fz(;)p Fx(\003)1343 2400 y Fu(N)p 1114 2417 V 1114 2493 a FA(Z)1171 2505 y Fx(+)p Fz(;\025;)p Fx(\003)1346 2513 y Fu(N)1436 2436 y FB(=)c(exp)1665 2294 y Fw(\()1732 2436 y Fy(\000)1811 2323 y Fw(Z)1893 2344 y Fz(\025)1856 2512 y Fx(0)1950 2436 y FB(d)p FA(\025)2044 2402 y Fv(0)2113 2357 y Fw(X)2082 2535 y Fz(x)p Fv(2)p Fx(\003)2210 2543 y Fu(N)2263 2436 y Fy(h)p FA(\033)2342 2448 y Fz(x)2385 2436 y Fy(i)2417 2448 y Fx(+)p Fz(;\025)2527 2432 y Fn(0)2549 2448 y Fz(;)p Fx(\003)2614 2456 y Fu(N)2672 2294 y Fw(\))2767 2436 y FA(;)515 2695 y FB(and,)k(similarly)-7 b(,)627 2886 y FA(Z)684 2898 y Fv(\006)p Fz(;\025;)p Fx(\003)860 2906 y Fu(N)931 2886 y FB(\()q Fy(j)p FA(C)1052 2856 y Fv(\000)1108 2886 y FB(\()14 b Fy(\001)g FB(\))p Fy(j)24 b(\025)e FA(V)d FB(\))p 627 2923 830 4 v 630 2999 a FA(Z)687 3011 y Fv(\006)p Fz(;)p Fx(0)p Fz(;)p Fx(\003)857 3019 y Fu(N)928 2999 y FB(\()q Fy(j)p FA(C)1049 2975 y Fv(\000)1105 2999 y FB(\()14 b Fy(\001)g FB(\))p Fy(j)23 b(\025)g FA(V)c FB(\))1489 2942 y(=)k(exp)1718 2800 y Fw(\()1785 2829 y(Z)1868 2849 y Fz(\025)1831 3018 y Fx(0)1925 2942 y FB(d)p FA(\025)2019 2908 y Fv(0)2087 2863 y Fw(X)2057 3041 y Fz(x)p Fv(2)p Fx(\003)2185 3049 y Fu(N)2238 2942 y Fy(h)p FA(\033)2317 2954 y Fz(x)2373 2942 y Fy(j)14 b(j)p FA(C)2498 2908 y Fv(\000)2554 2942 y FB(\()g Fy(\001)g FB(\))p Fy(j)24 b(\025)e FA(V)d Fy(i)2902 2954 y Fv(\006)p Fz(;\025)3013 2938 y Fn(0)3036 2954 y Fz(;)p Fx(\003)3101 2962 y Fu(N)3159 2800 y Fw(\))3253 2942 y FA(:)515 3201 y FB(W)-7 b(e)32 b(estimate)h(the)f(pro)r(duct)h(of)f(these)g(t)n(w)n (o)g(expressions)e(using)i(a)g(coupling)g(argumen)n(t.)515 3300 y(Since,)c(b)n(y)f(FK)n(G)g(inequalities)g(and)h(the)g(fact)g (that)g Fy(fj)p FA(C)2294 3270 y Fv(\000)2349 3300 y FB(\()14 b Fy(\001)g FB(\))p Fy(j)24 b(\025)e FA(V)d Fy(g)28 b FB(is)f(non-increasing,)1261 3477 y FA(\026)1311 3489 y Fx(+)p Fz(;\025)1421 3473 y Fn(0)1444 3489 y Fz(;)p Fx(\003)1509 3497 y Fu(N)1589 3477 y Fy(\027)c FA(\026)1727 3489 y Fv(\006)p Fz(;\025)1838 3473 y Fn(0)1861 3489 y Fz(;)p Fx(\003)1926 3497 y Fu(N)1983 3477 y FB(\()14 b Fy(\001)g(j)g(j)p FA(C)2191 3443 y Fv(\000)2247 3477 y FB(\()g Fy(\001)g FB(\))p Fy(j)24 b(\025)e FA(V)d FB(\))14 b FA(;)515 3654 y FB(there)27 b(exists)g(a)h(coupling)f FA(\027)1399 3666 y Fz(\025)1438 3650 y Fn(0)1492 3654 y FB(of)h FA(\026)1637 3666 y Fx(+)p Fz(;)p Fx(0)p Fz(;)p Fx(\003)1806 3674 y Fu(N)1891 3654 y FB(and)f FA(\026)2102 3666 y Fv(\006)p Fz(;\025)2213 3650 y Fn(0)2236 3666 y Fz(;)p Fx(\003)2301 3674 y Fu(N)2359 3654 y FB(\()14 b Fy(\001)g(j)g(j)p FA(C)2567 3624 y Fv(\000)2623 3654 y FB(\()g Fy(\001)g FB(\))p Fy(j)23 b(\025)g FA(V)c FB(\))28 b(suc)n(h)f(that)1638 3831 y FA(\027)5 b FB(\()p Fy(f)p FA(\033)27 b Fy(\025)22 b FA(\033)1969 3796 y Fv(0)1993 3831 y Fy(g)p FB(\))h(=)f(1)14 b FA(:)515 4008 y FB(In)37 b(fact,)i(it)e(is)g(w)n(ell-kno)n(wn)f(that)h(one)f(can)h(construct)f (this)h(coupling)g(explicitly)-7 b(.)65 b(W)-7 b(e)515 4107 y(quic)n(kly)36 b(sk)n(etc)n(h)f(this,)40 b(b)r(ecause)c(w)n(e'll) g(need)h(some)f(non-degeneracy)e(prop)r(ert)n(y)h(b)r(elo)n(w.)515 4207 y(First,)44 b(w)n(e)d(order)f(all)h(the)h(sites)f(in)h(\003)1778 4219 y Fz(N)1841 4207 y FB(,)i(sa)n(y)d FA(i)2095 4219 y Fx(1)2131 4207 y FA(;)14 b(:)g(:)g(:)g(;)g(i)2345 4222 y Fv(j)p Fx(\003)2410 4230 y Fu(N)2463 4222 y Fv(j)2487 4207 y FB(.)78 b(Then)42 b(w)n(e)f(in)n(tro)r(duce)f(a)515 4331 y(family)31 b(\()p FA(X)873 4343 y Fz(i)896 4352 y Fu(k)937 4331 y FB(\))969 4288 y Fv(j)p Fx(\003)1034 4296 y Fu(N)1088 4288 y Fv(j)969 4356 y Fz(k)q Fx(=1)1143 4331 y FB(of)g(iid)g(random)g(v)-5 b(ariables,)30 b(with)i(uniform)f (distribution)h(o)n(v)n(er)d([0)p FA(;)14 b FB(1].)515 4431 y(No)n(w)39 b(w)n(e)g(set)g FA(\033)1038 4443 y Fz(i)1061 4451 y Fm(1)1142 4431 y FB(=)j(1)e(\(resp.)72 b FA(\033)1657 4401 y Fv(0)1654 4453 y Fz(i)1677 4461 y Fm(1)1757 4431 y FB(=)43 b(1\))c(if)h FA(\026)2116 4443 y Fx(+)p Fz(;\025)2226 4427 y Fn(0)2249 4443 y Fz(;)p Fx(\003)2314 4451 y Fu(N)2371 4431 y FB(\()p FA(\033)2450 4443 y Fz(i)2473 4451 y Fm(1)2554 4431 y FB(=)j(1\))f Fy(\025)h FA(X)2955 4443 y Fz(i)2978 4451 y Fm(1)3054 4431 y FB(\(resp.)73 b(if)515 4531 y FA(\026)565 4543 y Fv(\006)p Fz(;\025)676 4526 y Fn(0)698 4543 y Fz(;)p Fx(\003)763 4551 y Fu(N)821 4531 y FB(\()p FA(\033)900 4543 y Fz(i)923 4551 y Fm(1)998 4531 y FB(=)37 b(1)14 b Fy(j)g(j)p FA(C)1281 4500 y Fv(\000)1337 4531 y FB(\()g Fy(\001)g FB(\))p Fy(j)38 b(\025)f FA(V)19 b FB(\))37 b Fy(\025)h FA(X)1923 4543 y Fz(i)1946 4551 y Fm(1)1982 4531 y FB(\);)j(otherwise)36 b(it)g(is)h(set)f(to)g Fy(\000)p FB(1.)62 b(Supp)r(ose)515 4630 y(w)n(e)39 b(ha)n(v)n(e)g(already)f (constructed)i(the)g(\014rst)g FA(k)29 b Fy(\000)d FB(1)40 b(spins.)74 b(Then)40 b(w)n(e)f(set)h FA(\033)3033 4642 y Fz(i)3056 4651 y Fu(k)3141 4630 y FB(=)j(1)d(if)515 4730 y FA(\026)565 4742 y Fx(+)p Fz(;\025)675 4726 y Fn(0)697 4742 y Fz(;)p Fx(\003)762 4750 y Fu(N)820 4730 y FB(\()p FA(\033)899 4742 y Fz(i)922 4751 y Fu(k)987 4730 y FB(=)22 b(1)14 b Fy(j)g FA(\033)1214 4742 y Fz(i)1237 4751 y Fu(l)1266 4730 y FA(;)27 b(l)e(<)e(k)s FB(\))g Fy(\025)f FA(X)1711 4742 y Fz(i)1734 4751 y Fu(k)1775 4730 y FB(,)k(and)g(similarly)e(for)h FA(\033)2496 4700 y Fv(0)2493 4751 y Fz(i)2516 4760 y Fu(k)2558 4730 y FB(.)36 b(Just)25 b(observ)n(e)f(that,)i(b)n(y)515 4829 y(FK)n(G)h(inequalities,)607 5006 y FA(\026)657 5018 y Fx(+)p Fz(;\025)767 5002 y Fn(0)790 5018 y Fz(;)p Fx(\003)855 5026 y Fu(N)912 5006 y FB(\()p FA(\033)991 5018 y Fz(i)1014 5027 y Fu(k)1079 5006 y FB(=)c(1)14 b Fy(j)g FA(\033)1307 5018 y Fz(i)1330 5027 y Fu(l)1358 5006 y FA(;)28 b(l)c(<)f(k)s FB(\))g Fy(\025)g FA(\026)1785 5018 y Fv(\006)p Fz(;\025)1896 5002 y Fn(0)1918 5018 y Fz(;)p Fx(\003)1983 5026 y Fu(N)2041 5006 y FB(\()p FA(\033)2120 5018 y Fz(i)2143 5027 y Fu(k)2208 5006 y FB(=)f(1)14 b Fy(j)g(j)p FA(C)2476 4972 y Fv(\000)2532 5006 y FB(\()g Fy(\001)g FB(\))p Fy(j)23 b(\025)g FA(V)5 b(;)28 b(\033)2932 5018 y Fz(i)2955 5027 y Fu(l)2984 5006 y FA(;)g(l)c(<)f(k)s FB(\))14 b FA(:)p Black Black eop end %%Page: 25 25 TeXDict begin 25 24 bop Black 515 232 a Fr(En)n(tropic)22 b(repulsion)g(in)f(external)h(\014eld;)g(v)n(ersion)f(from)g(July)g(3,) f(2003)1118 b FB(25)p Black 639 523 a(Using)44 b(this)g(notation,)k(w)n (e)43 b(are)g(left)h(with)h(estimating)2525 461 y Fw(P)2613 548 y Fz(x)p Fv(2)p Fx(\003)2741 556 y Fu(N)2812 523 y FB(\()p FA(\027)2885 535 y Fz(\025)2924 519 y Fn(0)2951 523 y FB(\()p FA(\033)3033 493 y Fv(0)3030 544 y Fz(x)3091 523 y Fy(\000)18 b FA(\033)3221 535 y Fz(x)3264 523 y FB(\)\))28 b FA(:)515 623 y FB(Since)g FA(\027)773 635 y Fz(\025)812 619 y Fn(0)839 623 y FB(\()p FA(\033)e Fy(\025)d FA(\033)1082 593 y Fv(0)1106 623 y FB(\))g(=)g(1,)k(w)n(e)g (can)g(write)1106 797 y FA(\027)1147 809 y Fz(\025)1186 793 y Fn(0)1213 730 y Fw(\000)1281 718 y(X)1251 896 y Fz(x)p Fv(2)p Fx(\003)1379 904 y Fu(N)1432 797 y FB(\()p FA(\033)1514 763 y Fv(0)1511 817 y Fz(x)1572 797 y Fy(\000)18 b FA(\033)1702 809 y Fz(x)1744 797 y FB(\))1776 730 y Fw(\001)1838 797 y Fy(\024)k FA(\027)1966 809 y Fz(\025)2005 793 y Fn(0)2032 730 y Fw(\000)2159 718 y(X)2070 901 y Fz(x)p Fv(2)p Fz(C)2205 884 y Fn(\000)2254 901 y Fx(\()p Fz(\033)2320 884 y Fn(0)2342 901 y Fx(\))2368 797 y FB(\()p FA(\033)2450 763 y Fv(0)2447 817 y Fz(x)2508 797 y Fy(\000)c FA(\033)2638 809 y Fz(x)2681 797 y FB(\))2713 730 y Fw(\001)2765 797 y FA(:)515 1056 y FB(No)n(w)31 b(observ)n(e)e(that)1191 993 y Fw(P)1278 1081 y Fz(x)p Fv(2)p Fz(C)1413 1064 y Fn(\000)1462 1081 y Fx(\()p Fz(\033)1528 1064 y Fn(0)1551 1081 y Fx(\))1595 1056 y FA(\033)1645 1026 y Fv(0)1642 1076 y Fz(x)1713 1056 y FB(=)g Fy(\000j)p FA(C)1960 1026 y Fv(\000)2016 1056 y FB(\()p FA(\033)2098 1026 y Fv(0)2122 1056 y FB(\))p Fy(j)p FB(.)48 b(Moreo)n(v)n(er,)30 b(from)h(the)h(ab)r (o)n(v)n(e)e(con-)515 1155 y(struction,)d(w)n(e)g(see)g(that)h(the)g (coupling)f(satis\014es)914 1313 y(inf)874 1366 y Fz(x)p Fv(2)p Fx(\003)1002 1374 y Fu(N)1069 1313 y FA(\027)1110 1325 y Fz(\025)1149 1309 y Fn(0)1176 1246 y Fw(\000)1214 1313 y FA(\033)1261 1325 y Fz(x)1340 1242 y Fw(\014)1340 1292 y(\014)1405 1313 y FA(\033)1452 1325 y Fz(y)1492 1313 y FA(;)h Fy(8)p FA(y)e Fy(2)d FB(\003)1792 1325 y Fz(N)1873 1313 y Fy(n)18 b(f)p FA(x)p Fy(g)p FA(;)c(\033)2151 1279 y Fv(0)2148 1333 y Fz(z)2187 1313 y FA(;)27 b Fy(8)p FA(z)g Fy(2)c FB(\003)2485 1325 y Fz(N)2548 1246 y Fw(\001)2609 1313 y FA(>)f Fy(\000)p FB(1)c Fy(\000)g FA(\017)2938 1325 y Fz(\014)2996 1313 y FA(;)515 1507 y FB(with)28 b FA(\017)738 1519 y Fz(\014)811 1507 y FB(dep)r(ending)g(only)f(on)h (the)g(parameter)f FA(\014)t FB(,)h(for)g(all)f FA(\025)i FB(small)e(enough.)37 b(Therefore,)515 1607 y(putting)28 b(ev)n(erything)e(together,)h(w)n(e)g(obtain)1074 1779 y FA(\026)1124 1791 y Fv(\006)p Fz(;\025;)p Fx(\003)1300 1799 y Fu(N)1372 1712 y Fw(\000)1410 1779 y Fy(j)p FA(C)1498 1745 y Fv(\000)1554 1779 y FB(\()14 b Fy(\001)g FB(\))p Fy(j)23 b(\025)g FA(V)1870 1712 y Fw(\001)1931 1779 y Fy(\024)g FA(e)2058 1745 y Fv(\000)p Fx(\()p Fz(K)t(\017)2224 1754 y Fu(\014)2262 1745 y Fv(\000)p Fz(c)p Fx(\))p Fv(j)10 b Fx(log)j Fz(\025)p Fv(j)2557 1720 y Fm(2)2589 1745 y Fz(\025)2628 1720 y Fm(2)p Fu(=)p Fm(3)2720 1745 y Fz(N)2797 1779 y FA(;)515 1937 y FB(and)27 b(the)h(conclusion)f(follo)n (ws)f(once)i FA(K)33 b FB(is)27 b(tak)n(en)g(large)f(enough.)515 2207 y FD(A)134 b(Some)45 b(to)t(ols)515 2389 y FB(In)27 b(this)h(section)f(w)n(e)g(collect)h(sev)n(eral)d(results)i(from)h([26) o(,)f(29)o(,)h(27)o(])g(whic)n(h)f(w)n(e)g(are)g(using)g(in)515 2489 y(the)d(pap)r(er.)35 b(This)24 b(is)g(not)f(supp)r(osed)h(to)g(b)r (e)g(an)f(in)n(tro)r(duction)h(to)g(the)g(random-line)e(repre-)515 2588 y(sen)n(tation,)k(and)g(w)n(e)g(refer)g(the)g(reader)f(to)h(the)h (latter)f(w)n(orks)f(for)h(detailed)g(explanations.)639 2688 y(Let)31 b Fy(E)842 2658 y Fv(\003)911 2688 y FB(b)r(e)g(the)g (set)g(of)f(all)g(dual)h(b)r(onds)f(of)h(the)g(in\014nite)g(lattice.)46 b(One)30 b(of)h(the)g(basic)515 2788 y(ob)5 b(jects)24 b(in)g(this)h(pap)r(er)f(is)g(the)h(partition)f(function)h FA(Z)2220 2800 y Fv(\006)p Fz(;\014)s(;\025;h;)p Fx(\003)2516 2808 y Fu(N)2572 2788 y FB(.)36 b(T)-7 b(o)24 b(an)n(y)g (con\014guration)515 2887 y FA(\033)31 b FB(with)d(non-zero)e(w)n(eigh) n(t)h(under)g FA(\026)1667 2899 y Fv(\006)p Fz(;\014)s(;\025;h;)p Fx(\003)1963 2907 y Fu(N)2020 2887 y FB(,)h(w)n(e)f(can)g(asso)r(ciate) f(a)h(subset)h FA(n)p FB(\()p FA(\033)s FB(\))g(of)1099 3045 y Fy(E)1150 3011 y Fv(\003)1143 3065 y Fz(N)1229 3045 y FB(=)23 b Fy(f)p FA(e)1398 3011 y Fv(\003)1458 3045 y Fy(2)h(E)1588 3011 y Fv(\003)1663 3045 y FB(:)37 b FA(e)1762 3011 y Fv(\003)1827 3045 y FB(dual)28 b(to)f FA(e)c Fy(\032)g FB(\003)2321 3057 y Fz(N)2383 3045 y FA(;)28 b(e)23 b Fy(6\032)f FA(@)5 b FB(\003)2690 3057 y Fz(N)2753 3045 y Fy(g)515 3202 y FB(comp)r(osed)39 b(of)h(all)g(dual)f(edges)h FA(e)1613 3172 y Fv(\003)1690 3202 y FB(suc)n(h)g(that)g FA(e)j FB(=)h Fy(h)p FA(x;)14 b(y)s Fy(i)44 b(6\032)f FA(@)5 b FB(\003)2724 3214 y Fz(N)2826 3202 y FB(with)41 b FA(\033)3075 3214 y Fz(x)3160 3202 y Fy(6)p FB(=)j FA(\033)3316 3214 y Fz(y)3356 3202 y FB(.)515 3302 y(W)-7 b(e)35 b(then)h(split)g(this)g(subset)f(in)n(to) g(a)g(collection)g(of)g(con)n(tours,)h(b)n(y)f(applying)g(the)h(rules) 515 3402 y(giv)n(en)29 b(in)h(Fig.)f(5)h(eac)n(h)f(time)h(more)f(than)h (t)n(w)n(o)f(b)r(onds)g(are)g(inciden)n(t)h(on)g(a)f(giv)n(en)g(v)n (ertex;)515 3501 y(con)n(tours)h(are)h(the)i(families)f(of)g(edges)f (remaining)h(connected)f(after)h(these)g(op)r(erations.)515 3601 y(Among)k(all)g(the)g(con)n(tours,)h(there)g(is)f(a)g(unique)g(op) r(en)h(con)n(tour)e(connecting)g(the)i(dual)515 3700 y(sites)27 b(\()p Fy(\000)p FB(\()p FA(N)h Fy(\000)18 b FB(1\))p FA(=)p FB(2)p FA(;)c FB(1)p FA(=)p FB(2\))25 b(and)i(\(\()p FA(N)h FB(+)18 b(1\))p FA(=)p FB(2)p FA(;)c FB(1)p FA(=)p FB(2\);)25 b(w)n(e)i(call)h(it)g FA(\015)5 b FB(.)639 3800 y(W)-7 b(e)30 b(w)n(an)n(t)e(to)h(expand)f(the)i (partition)e(functions)i(in)f(terms)f(of)h(the)h(op)r(en)f(con)n(tour)e FA(\015)5 b FB(.)515 3900 y(Notice)24 b(that)g(once)f FA(\015)28 b FB(is)c(\014xed,)h(some)e(spins)h(in)g(the)g(b)r(o)n(x)f (\003)2359 3912 y Fz(N)2446 3900 y FB(b)r(ecome)h(frozen)f(\(i.e.)36 b(in)24 b(an)n(y)515 3999 y(con\014guration)31 b(with)i(p)r(ositiv)n(e) f(w)n(eigh)n(t)h(ha)n(ving)e FA(\015)38 b FB(as)32 b(op)r(en)h(con)n (tour,)f(these)h(spins)g(tak)n(e)515 4099 y(the)f(same)f(v)-5 b(alues\).)50 b(W)-7 b(e)32 b(denote)f(b)n(y)h(\003)1795 4069 y Fx(+)1850 4099 y FB(\()p FA(\015)5 b FB(\))32 b(the)g(set)g(of)g(all)f(non-frozen)g(spins)g(lo)r(cated)515 4199 y(inside)g(a)g(comp)r(onen)n(t)g(surrounded)f(b)n(y)h(+)g(spins.) 48 b(Similarly)-7 b(,)32 b(w)n(e)f(write)g(\003)2934 4168 y Fv(\000)2989 4199 y FB(\()p FA(\015)5 b FB(\))32 b(for)f(the)515 4298 y(set)c(of)h(all)f(non-frozen)g(spins)g(lo)r (cated)g(inside)h(a)f(comp)r(onen)n(t)h(surrounded)e(b)n(y)h Fy(\000)h FB(spins.)639 4398 y(W)-7 b(e)28 b(then)g(ha)n(v)n(e)1032 4555 y FA(Z)1089 4567 y Fv(\006)p Fz(;\014)s(;\025;h;)p Fx(\003)1385 4575 y Fu(N)1464 4555 y FB(=)1552 4477 y Fw(X)1592 4651 y Fz(\015)1685 4555 y FA(w)r FB(\()p FA(\015)5 b FB(\))24 b FA(Z)1939 4571 y Fx(+)p Fz(;\014)s(;\025;)p Fx(\003)2175 4554 y Fm(+)2221 4571 y Fx(\()p Fz(\015)t Fx(\))2330 4555 y FA(Z)2387 4571 y Fv(\000)p Fz(;\014)s(;\025;h;)p Fx(\003)2683 4554 y Fn(\000)2731 4571 y Fx(\()p Fz(\015)t Fx(\))2839 4555 y FA(;)284 b FB(\(A.11\))515 4794 y(where)23 b FA(Z)808 4810 y Fx(+)p Fz(;\014)s(;\025;)p Fx(\003)1044 4793 y Fm(+)1090 4810 y Fx(\()p Fz(\015)t Fx(\))1209 4794 y FB(and)h FA(Z)1424 4810 y Fv(\000)p Fz(;\014)s(;\025;h;)p Fx(\003)1720 4793 y Fn(\000)1768 4810 y Fx(\()p Fz(\015)t Fx(\))1886 4794 y FB(are)g(the)g(t)n(w)n(o)f(partition)h(functions)g (asso)r(ciated)515 4907 y(to)f(the)i(restriction)e(of)g(our)h(system)f (to)h(\003)1808 4876 y Fx(+)1863 4907 y FB(\()p FA(\015)5 b FB(\))24 b(and)g(\003)2215 4876 y Fv(\000)2270 4907 y FB(\()p FA(\015)5 b FB(\),)25 b(and)f FA(w)r FB(\()p FA(\015)5 b FB(\))24 b(=)f FA(e)2912 4876 y Fv(\000)p Fx(2)p Fz(\014)s Fv(j)p Fz(\015)t Fv(j)3119 4907 y FB(,)i(where)515 5006 y Fy(j)p FA(\015)5 b Fy(j)23 b FB(=)719 4944 y Fw(P)807 5031 y Fz(e)838 5015 y Fn(\003)873 5031 y Fv(\032)p Fz(\015)981 5006 y FA(J)8 b FB(\()p FA(e)p FB(\).)p Black Black eop end %%Page: 26 26 TeXDict begin 26 25 bop Black 515 232 a Fr(En)n(tropic)22 b(repulsion)g(in)f(external)h(\014eld;)g(v)n(ersion)f(from)g(July)g(3,) f(2003)1118 b FB(26)p Black Black 1053 1267 a @beginspecial 0 @llx 0 @lly 636 @urx 294 @ury 992 @rhi @setspecial %%BeginDocument: rules.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: rules.eps %%Creator: fig2dev Version 3.2.3 Patchlevel %%CreationDate: Fri Sep 14 13:48:31 2001 %%For: velenik@latpcmi22.cmi.univ-mrs.fr (Yvan VELENIK, CR probabilites) %%BoundingBox: 0 0 636 294 %%Magnification: 1.0000 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save newpath 0 294 moveto 0 0 lineto 636 0 lineto 636 294 lineto closepath clip newpath % Fill background color 0 0 moveto 636 0 lineto 636 294 lineto 0 294 lineto closepath 1.00 1.00 1.00 setrgbcolor fill -96.0 444.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def $F2psBegin %%Page: 1 1 10 setmiterlimit 0.06000 0.06000 sc % Polyline 30.000 slw n 2400 6000 m 2400 7200 l gs col1 s gr % Polyline n 2400 6600 m 1800 6600 l gs col1 s gr % Polyline n 5400 6600 m 5400 6000 l gs col1 s gr % Polyline n 5400 7200 m 5400 7197 l 5400 7190 l 5400 7177 l 5399 7158 l 5399 7135 l 5398 7107 l 5398 7076 l 5397 7044 l 5396 7012 l 5395 6982 l 5393 6954 l 5392 6928 l 5390 6904 l 5388 6882 l 5386 6863 l 5384 6845 l 5381 6829 l 5378 6814 l 5375 6800 l 5370 6783 l 5365 6767 l 5359 6752 l 5352 6737 l 5344 6723 l 5335 6710 l 5326 6697 l 5315 6685 l 5303 6674 l 5290 6665 l 5277 6656 l 5263 6648 l 5248 6641 l 5233 6635 l 5217 6630 l 5200 6625 l 5186 6622 l 5171 6619 l 5155 6616 l 5137 6614 l 5118 6612 l 5096 6610 l 5072 6608 l 5046 6607 l 5018 6605 l 4987 6604 l 4956 6603 l 4924 6602 l 4893 6602 l 4865 6601 l 4842 6601 l 4823 6600 l 4810 6600 l 4803 6600 l 4800 6600 l gs col1 s gr % Polyline n 8400 7200 m 8400 6000 l gs col1 s gr % Polyline n 8400 6600 m 9000 6600 l gs col1 s gr % Polyline n 9000 5400 m 7800 5400 l gs col1 s gr % Polyline n 8400 5400 m 8400 4800 l gs col1 s gr % Polyline n 11400 5400 m 10800 5400 l gs col1 s gr % Polyline n 12000 5400 m 11997 5400 l 11990 5400 l 11977 5400 l 11958 5399 l 11935 5399 l 11907 5398 l 11876 5398 l 11844 5397 l 11812 5396 l 11782 5395 l 11754 5393 l 11728 5392 l 11704 5390 l 11682 5388 l 11663 5386 l 11645 5384 l 11629 5381 l 11614 5378 l 11600 5375 l 11583 5370 l 11567 5365 l 11552 5359 l 11537 5352 l 11523 5344 l 11510 5335 l 11497 5326 l 11485 5315 l 11474 5303 l 11465 5290 l 11456 5277 l 11448 5263 l 11441 5248 l 11435 5233 l 11430 5217 l 11425 5200 l 11422 5186 l 11419 5171 l 11416 5155 l 11414 5137 l 11412 5118 l 11410 5096 l 11408 5072 l 11407 5046 l 11405 5018 l 11404 4987 l 11403 4956 l 11402 4924 l 11402 4893 l 11401 4865 l 11401 4842 l 11400 4823 l 11400 4810 l 11400 4803 l 11400 4800 l gs col1 s gr % Polyline n 11400 6600 m 11400 7200 l gs col1 s gr % Polyline n 11400 6000 m 11400 6003 l 11400 6010 l 11400 6023 l 11401 6042 l 11401 6065 l 11402 6093 l 11402 6124 l 11403 6156 l 11404 6188 l 11405 6218 l 11407 6246 l 11408 6272 l 11410 6296 l 11412 6318 l 11414 6337 l 11416 6355 l 11419 6371 l 11422 6386 l 11425 6400 l 11430 6417 l 11435 6433 l 11441 6448 l 11448 6463 l 11456 6477 l 11465 6490 l 11474 6503 l 11485 6515 l 11497 6526 l 11510 6535 l 11523 6544 l 11537 6552 l 11552 6559 l 11567 6565 l 11583 6570 l 11600 6575 l 11614 6578 l 11629 6581 l 11645 6584 l 11663 6586 l 11682 6588 l 11704 6590 l 11728 6592 l 11754 6593 l 11782 6595 l 11813 6596 l 11844 6597 l 11876 6598 l 11907 6598 l 11935 6599 l 11958 6599 l 11977 6600 l 11990 6600 l 11997 6600 l 12000 6600 l gs col1 s gr % Polyline gs clippath 10290 5145 m 10290 5055 l 10030 5055 l 10255 5100 l 10030 5145 l cp eoclip n 9675 5100 m 10275 5100 l gs col0 s gr gr % arrowhead 7.500 slw n 10030 5145 m 10255 5100 l 10030 5055 l 10075 5100 l 10030 5145 l cp gs -0.00 setgray ef gr col0 s % Polyline 30.000 slw gs clippath 4215 5145 m 4215 5055 l 3955 5055 l 4180 5100 l 3955 5145 l cp eoclip n 3600 5100 m 4200 5100 l gs col0 s gr gr % arrowhead 7.500 slw n 3955 5145 m 4180 5100 l 3955 5055 l 4000 5100 l 3955 5145 l cp gs -0.00 setgray ef gr col0 s % Polyline 30.000 slw gs clippath 4215 6645 m 4215 6555 l 3955 6555 l 4180 6600 l 3955 6645 l cp eoclip n 3600 6600 m 4200 6600 l gs col0 s gr gr % arrowhead 7.500 slw n 3955 6645 m 4180 6600 l 3955 6555 l 4000 6600 l 3955 6645 l cp gs -0.00 setgray ef gr col0 s % Polyline 30.000 slw gs clippath 10215 6645 m 10215 6555 l 9955 6555 l 10180 6600 l 9955 6645 l cp eoclip n 9600 6600 m 10200 6600 l gs col0 s gr gr % arrowhead 7.500 slw n 9955 6645 m 10180 6600 l 9955 6555 l 10000 6600 l 9955 6645 l cp gs -0.00 setgray ef gr col0 s % Polyline 30.000 slw n 2400 4800 m 2400 5400 l gs col1 s gr % Polyline n 3000 4800 m 1800 4800 l gs col1 s gr % Polyline n 5400 4800 m 6000 4800 l gs col1 s gr % Polyline n 5400 2700 m 5400 3900 l gs col1 s gr % Polyline n 6000 3300 m 4800 3300 l gs col1 s gr % Polyline gs clippath 7215 3345 m 7215 3255 l 6955 3255 l 7180 3300 l 6955 3345 l cp eoclip n 6600 3300 m 7200 3300 l gs col0 s gr gr % arrowhead 7.500 slw n 6955 3345 m 7180 3300 l 6955 3255 l 7000 3300 l 6955 3345 l cp gs -0.00 setgray ef gr col0 s % Polyline 30.000 slw n 5400 5400 m 5400 5397 l 5400 5390 l 5400 5377 l 5399 5358 l 5399 5335 l 5398 5307 l 5398 5276 l 5397 5244 l 5396 5212 l 5395 5182 l 5393 5154 l 5392 5128 l 5390 5104 l 5388 5082 l 5386 5063 l 5384 5045 l 5381 5029 l 5378 5014 l 5375 5000 l 5370 4983 l 5365 4967 l 5359 4952 l 5352 4937 l 5344 4923 l 5335 4910 l 5326 4897 l 5315 4885 l 5303 4874 l 5290 4865 l 5277 4856 l 5263 4848 l 5248 4841 l 5233 4835 l 5217 4830 l 5200 4825 l 5186 4822 l 5171 4819 l 5155 4816 l 5137 4814 l 5118 4812 l 5096 4810 l 5072 4808 l 5046 4807 l 5018 4805 l 4987 4804 l 4956 4803 l 4924 4802 l 4893 4802 l 4865 4801 l 4842 4801 l 4823 4800 l 4810 4800 l 4803 4800 l 4800 4800 l gs col1 s gr % Polyline n 8400 3900 m 8400 3897 l 8400 3890 l 8400 3877 l 8399 3858 l 8399 3835 l 8398 3807 l 8398 3776 l 8397 3744 l 8396 3712 l 8395 3682 l 8393 3654 l 8392 3628 l 8390 3604 l 8388 3582 l 8386 3563 l 8384 3545 l 8381 3529 l 8378 3514 l 8375 3500 l 8370 3483 l 8365 3467 l 8359 3452 l 8352 3437 l 8344 3423 l 8335 3410 l 8326 3397 l 8315 3385 l 8303 3374 l 8290 3365 l 8277 3356 l 8263 3348 l 8248 3341 l 8233 3335 l 8217 3330 l 8200 3325 l 8186 3322 l 8171 3319 l 8155 3316 l 8137 3314 l 8118 3312 l 8096 3310 l 8072 3308 l 8046 3307 l 8018 3305 l 7987 3304 l 7956 3303 l 7924 3302 l 7893 3302 l 7865 3301 l 7842 3301 l 7823 3300 l 7810 3300 l 7803 3300 l 7800 3300 l gs col1 s gr % Polyline n 9000 3300 m 8997 3300 l 8990 3300 l 8977 3300 l 8958 3299 l 8935 3299 l 8907 3298 l 8876 3298 l 8844 3297 l 8812 3296 l 8782 3295 l 8754 3293 l 8728 3292 l 8704 3290 l 8682 3288 l 8663 3286 l 8645 3284 l 8629 3281 l 8614 3278 l 8600 3275 l 8583 3270 l 8567 3265 l 8552 3259 l 8537 3252 l 8523 3244 l 8510 3235 l 8497 3226 l 8485 3215 l 8474 3203 l 8465 3190 l 8456 3177 l 8448 3163 l 8441 3148 l 8435 3133 l 8430 3117 l 8425 3100 l 8422 3086 l 8419 3071 l 8416 3055 l 8414 3037 l 8412 3018 l 8410 2996 l 8408 2972 l 8407 2946 l 8405 2918 l 8404 2887 l 8403 2856 l 8402 2824 l 8402 2793 l 8401 2765 l 8401 2742 l 8400 2723 l 8400 2710 l 8400 2703 l 8400 2700 l gs col1 s gr $F2psEnd rs %%EndDocument @endspecial Black 1427 1449 a(Figure)27 b(5:)37 b(Deformation)27 b(rules.)p Black Black 639 1697 a(W)-7 b(e)28 b(in)n(tro)r(duce)f(the)h (w)n(eigh)n(t)f(\(notice)h(that)g(it)g(is)f(computed)h(at)g(zero)e (bulk)i(\014eld\))1134 1907 y FA(q)1171 1919 y Fz(\014)s(;h;N)1353 1907 y FB(\()p FA(\015)5 b FB(\))23 b(=)g FA(w)r FB(\()p FA(\015)5 b FB(\))1783 1844 y FA(Z)1840 1860 y Fx(+)p Fz(;\014)s(;)p Fx(0)p Fz(;)p Fx(\003)2070 1843 y Fm(+)2115 1860 y Fx(\()p Fz(\015)t Fx(\))2224 1844 y FA(Z)2281 1860 y Fv(\000)p Fz(;\014)s(;)p Fx(0)p Fz(;h;)p Fx(\003)2571 1843 y Fn(\000)2618 1860 y Fx(\()p Fz(\015)t Fx(\))p 1783 1888 931 4 v 2047 1964 a FA(Z)2104 1976 y Fx(+)p Fz(;\014)s(;)p Fx(0)p Fz(;h;)p Fx(\003)2393 1984 y Fu(N)2737 1907 y FA(:)386 b FB(\(A.12\))639 2120 y(Let)36 b FA(\014)847 2089 y Fv(\003)885 2120 y FB(,)h FA(h)993 2089 y Fv(\003)1067 2120 y FB(and)e FA(J)1290 2089 y Fv(\003)1328 2120 y FB(\()p FA(e)1399 2089 y Fv(\003)1437 2120 y FB(\))g(b)r(e)h(suc)n(h)f (that)g(tanh\()p FA(\014)2256 2089 y Fv(\003)2295 2120 y FB(\))h(=)g(exp)o(\()p Fy(\000)p FB(2)p FA(\014)t FB(\),)i(tanh\()p FA(\014)3122 2089 y Fv(\003)3160 2120 y FA(h)3208 2089 y Fv(\003)3246 2120 y FB(\))e(=)515 2219 y(exp\()p Fy(\000)p FB(2)p FA(\014)t(h)p FB(\))27 b(and)h(tanh\()p FA(\014)1350 2189 y Fv(\003)1388 2219 y FA(J)1442 2189 y Fv(\003)1481 2219 y FB(\()p FA(e)1552 2189 y Fv(\003)1590 2219 y FB(\)\))23 b(=)g(exp\()p Fy(\000)p FB(2)p FA(\014)t(J)8 b FB(\()p FA(e)p FB(\)\).)639 2319 y(The)28 b(Gibbs)g(measure)e(in)i Fy(E)1522 2289 y Fv(\003)1515 2342 y Fz(N)1606 2319 y FB(with)g(free)f(b.c.)37 b(is)28 b(de\014ned)g(b)n(y)958 2498 y FA(\026)1008 2510 y Fz(\014)1049 2494 y Fn(\003)1083 2510 y Fz(;h)1142 2494 y Fn(\003)1177 2510 y Fz(;N)1259 2498 y FB(\()p FA(\033)s FB(\))c(=)f(\()p FA(Z)1574 2510 y Fz(\014)1615 2494 y Fn(\003)1649 2510 y Fz(;h)1708 2494 y Fn(\003)1743 2510 y Fz(;N)1825 2498 y FB(\))1857 2464 y Fv(\000)p Fx(1)2107 2420 y Fw(Y)1961 2602 y Fz(e)1992 2585 y Fn(\003)2027 2602 y Fx(=)p Fv(h)p Fz(x;y)r Fv(i2E)2312 2582 y Fn(\003)2307 2621 y Fu(N)2372 2498 y FA(e)2411 2464 y Fv(\000)p Fz(\014)2504 2439 y Fn(\003)2538 2464 y Fz(J)2580 2439 y Fn(\003)2615 2464 y Fx(\()p Fz(e)2672 2439 y Fn(\003)2707 2464 y Fx(\))12 b Fz(\033)2783 2472 y Fu(x)2820 2464 y Fz(\033)2858 2472 y Fu(y)2913 2498 y FA(:)515 2761 y FB(A)28 b(basic)f(dualit)n(y)g(argumen)n(t,)g(see)g (e.g.)g(Lemma)g(6.2)g(in)h([27)o(],)g(sho)n(ws)e(that)855 2860 y Fw(X)895 3034 y Fz(\015)988 2939 y FA(q)1025 2951 y Fz(\014)s(;h;N)1207 2939 y FB(\()p FA(\015)5 b FB(\))23 b(=)g Fy(h)p FA(\033)1509 2954 y Fx(\()p Fv(\000)p Fx(\()p Fz(N)6 b Fv(\000)p Fx(1\))p Fz(=)p Fx(2)p Fz(;)p Fx(1)p Fz(=)p Fx(2\))2000 2939 y FA(\033)2047 2954 y Fx(\(\()p Fz(N)g Fx(+1\))p Fz(=)p Fx(2)p Fz(;)p Fx(1)p Fz(=)p Fx(2\))2486 2939 y Fy(i)2518 2951 y Fz(\014)2559 2935 y Fn(\003)2593 2951 y Fz(;h)2652 2935 y Fn(\003)2687 2951 y Fz(;N)2783 2939 y FA(:)340 b FB(\(A.13\))515 3181 y(One)23 b(has)f(in)i(fact)f(a)g (deep)r(er)g(relation)f(b)r(et)n(w)n(een)h(high)g(and)g(lo)n(w)f(temp)r (erature)h(mo)r(dels.)35 b(T)-7 b(o)515 3281 y(eac)n(h)31 b(subset)g(of)h Fy(E)1114 3251 y Fv(\003)1107 3304 y Fz(N)1202 3281 y FB(whic)n(h)f(remains)g(connected)h(after)f(applying)g (the)h(rules)f(of)h(Fig.)f(5,)515 3381 y(w)n(e)c(can)g(asso)r(ciate)f (a)i(w)n(eigh)n(t)e FA(q)1510 3350 y Fv(\003)1507 3404 y Fz(\014)1548 3387 y Fn(\003)1583 3404 y Fz(;h)1642 3387 y Fn(\003)1676 3404 y Fz(;N)1786 3381 y FB(\(see)i(\(6.8\))f(of)h ([27)o(])g(for)f(a)g(de\014nition\))h(suc)n(h)f(that)1507 3542 y FA(q)1547 3507 y Fv(\003)1544 3562 y Fz(\014)1585 3545 y Fn(\003)1620 3562 y Fz(;h)1679 3545 y Fn(\003)1713 3562 y Fz(;N)1796 3542 y FB(\()p FA(\015)5 b FB(\))23 b(=)f FA(q)2055 3554 y Fz(\014)s(;h;N)2237 3542 y FB(\()p FA(\015)5 b FB(\))14 b FA(:)515 3702 y FB(Ho)n(w)n(ev)n(er,)43 b FA(q)930 3672 y Fv(\003)927 3726 y Fz(\014)968 3709 y Fn(\003)1002 3726 y Fz(;h)1061 3709 y Fn(\003)1095 3726 y Fz(;N)1220 3702 y FB(b)r(eing)e(de\014ned)h(for)f(m)n(uc)n(h)g (more)g(general)f(subsets)h(of)h Fy(E)3116 3672 y Fv(\003)3109 3725 y Fz(N)3213 3702 y FB(than)515 3802 y FA(q)552 3814 y Fz(\014)s(;h;N)734 3802 y FB(,)25 b(it)f(is)h(a)e(m)n(uc)n(h)h(more)g (useful)g(quan)n(tit)n(y)-7 b(.)36 b(W)-7 b(e'll)25 b(state)f(its)g (prop)r(erties)f(for)h(arbitrary)515 3902 y FA(E)k Fi(b)23 b Fy(E)743 3872 y Fv(\003)781 3902 y FB(,)k(and)g(will)h(denote)f(the)g (corresp)r(onding)f(w)n(eigh)n(t)g(b)n(y)h FA(q)2509 3872 y Fv(\003)2506 3925 y Fz(\014)2547 3909 y Fn(\003)2581 3925 y Fz(;h)2640 3909 y Fn(\003)2675 3925 y Fz(;E)2750 3902 y FB(.)37 b(W)-7 b(e)28 b(list)f(no)n(w)g(the)515 4001 y(prop)r(erties)33 b(of)i(these)g(w)n(eigh)n(ts)f(that)g(w)n(e)h (are)e(using)i(in)g(the)g(pro)r(of.)57 b(Let)35 b(us)g(denote)f(b)n(y) 515 4101 y Fy(E)566 4071 y Fv(\003)559 4123 y Fx(s)p Fz(:)p Fx(i)p Fz(:)670 4101 y FB(=)758 4039 y Fw(S)827 4126 y Fz(N)6 b Fv(!1)1036 4101 y Fy(E)1087 4071 y Fv(\003)1080 4124 y Fz(N)1143 4101 y FB(.)p Black 639 4250 a Fy(\017)p Black 41 w FB(\([27],)45 b(Lemma)c(6.3\))h(The)f(limiting)h(w)n(eigh)n (ts)f FA(q)2300 4220 y Fv(\003)2297 4273 y Fz(\014)2338 4257 y Fn(\003)2372 4273 y Fz(;h)2431 4257 y Fn(\003)2516 4250 y FB(=)46 b(lim)2743 4262 y Fz(E)s Fv("E)2870 4246 y Fn(\003)2922 4250 y FA(q)2962 4220 y Fv(\003)2959 4273 y Fz(\014)3000 4257 y Fn(\003)3034 4273 y Fz(;h)3093 4257 y Fn(\003)3128 4273 y Fz(;E)3245 4250 y FB(and)722 4349 y FA(q)762 4319 y Fv(\003)759 4373 y Fz(\014)800 4356 y Fn(\003)835 4373 y Fz(;h)894 4356 y Fn(\003)928 4373 y Fz(;)p Fx(s)p Fz(:)p Fx(i)p Fz(:)1074 4349 y FB(=)36 b(lim)1291 4361 y Fz(E)s Fv("E)1418 4342 y Fn(\003)1413 4381 y Fm(s)p Fu(:)p Fm(i)p Fu(:)1512 4349 y FA(q)1552 4319 y Fv(\003)1549 4373 y Fz(\014)1590 4356 y Fn(\003)1625 4373 y Fz(;h)1684 4356 y Fn(\003)1718 4373 y Fz(;E)1830 4349 y FB(are)f(w)n(ell-de\014ned)h(quan)n(tities.)62 b(Moreo)n(v)n(er,)36 b(for)722 4449 y(an)n(y)27 b FA(\015)h Fy(\032)22 b FA(E)5 b FB(,)1351 4549 y FA(q)1391 4514 y Fv(\003)1388 4569 y Fz(\014)1429 4552 y Fn(\003)1463 4569 y Fz(;h)1522 4552 y Fn(\003)1556 4569 y Fz(;E)1632 4549 y FB(\()p FA(\015)g FB(\))23 b Fy(\025)g FA(q)1895 4514 y Fv(\003)1892 4569 y Fz(\014)1933 4552 y Fn(\003)1967 4569 y Fz(;h)2026 4552 y Fn(\003)2061 4569 y Fz(;)p Fx(s)p Fz(:)p Fx(i)p Fz(:)2169 4549 y FB(\()p FA(\015)5 b FB(\))23 b Fy(\025)g FA(q)2432 4514 y Fv(\003)2429 4569 y Fz(\014)2470 4552 y Fn(\003)2504 4569 y Fz(;h)2563 4552 y Fn(\003)2602 4549 y FB(\()p FA(\015)5 b FB(\))14 b FA(:)395 b FB(\(A.14\))p Black 639 4714 a Fy(\017)p Black 41 w FB(\([27],)27 b(Lemma)g(6.4\))f (If)h FA(\015)h FB(=)23 b FA(\015)1679 4726 y Fx(1)1733 4714 y Fy(q)17 b FA(\015)1855 4726 y Fx(2)1920 4714 y FB(\()p Fy(q)27 b FB(is)g(a)f(concatenation)g(op)r(eration,)g(see)h ([27)o(])722 4813 y(for)g(a)h(de\014nition\),)g(then)1347 4974 y FA(q)1387 4940 y Fv(\003)1384 4995 y Fz(\014)1425 4978 y Fn(\003)1459 4995 y Fz(;h)1518 4978 y Fn(\003)1552 4995 y Fz(;E)1628 4974 y FB(\()p FA(\015)5 b FB(\))24 b Fy(\025)e FA(q)1891 4940 y Fv(\003)1888 4995 y Fz(\014)1929 4978 y Fn(\003)1964 4995 y Fz(;h)2023 4978 y Fn(\003)2057 4995 y Fz(;E)2133 4974 y FB(\()p FA(\015)2208 4986 y Fx(1)2245 4974 y FB(\))14 b FA(q)2331 4940 y Fv(\003)2328 4995 y Fz(\014)2369 4978 y Fn(\003)2404 4995 y Fz(;h)2463 4978 y Fn(\003)2497 4995 y Fz(;E)2573 4974 y FB(\()p FA(\015)2648 4986 y Fx(2)2685 4974 y FB(\))g FA(:)392 b FB(\(A.15\))p Black Black eop end %%Page: 27 27 TeXDict begin 27 26 bop Black 515 232 a Fr(En)n(tropic)22 b(repulsion)g(in)f(external)h(\014eld;)g(v)n(ersion)f(from)g(July)g(3,) f(2003)1118 b FB(27)p Black Black 639 523 a Fy(\017)p Black 41 w FB(\([27],)27 b(Lemma)h(6.5\))f(Let)h FA(t)1576 535 y Fx(1)1613 523 y FA(;)14 b(:)g(:)g(:)f(;)h(t)1827 535 y Fz(n)1900 523 y FB(b)r(e)28 b(distinct)g(dual)g(sites)f(in)h FA(E)5 b FB(.)37 b(Then)1096 699 y Fw(X)964 874 y Fz(\015)t Fx(:)11 b Fz(t)1058 882 y Fm(1)1090 874 y Fv(!\001\001\001!)p Fz(t)1307 882 y Fu(n)1362 778 y FA(q)1402 744 y Fv(\003)1399 799 y Fz(\014)1440 782 y Fn(\003)1474 799 y Fz(;h)1533 782 y Fn(\003)1567 799 y Fz(;E)1643 778 y FB(\()p FA(\015)5 b FB(\))23 b Fy(\024)1866 674 y Fz(n)p Fv(\000)p Fx(1)1876 699 y Fw(Y)1869 878 y Fz(k)q Fx(=1)2173 699 y Fw(X)2006 873 y Fz(\015)t Fx(:)10 b Fz(t)2099 882 y Fu(k)2136 873 y Fv(!\001\001\001)o(!)p Fz(t)2352 882 y Fu(k)q Fm(+1)2473 778 y FA(q)2513 744 y Fv(\003)2510 799 y Fz(\014)2551 782 y Fn(\003)2586 799 y Fz(;h)2645 782 y Fn(\003)2679 799 y Fz(;E)2755 778 y FB(\()p FA(\015)5 b FB(\))14 b FA(:)242 b FB(\(A.16\))p Black 639 1076 a Fy(\017)p Black 41 w FB(\([29],)27 b(Lemma)f(4.4.6,)f(and)i([27)o(],)g(Lemma)f(6.10\))f (Let)i Fy(R)g FB(b)r(e)g(a)f(rectangular)e(subset)722 1176 y(of)c Fy(E)860 1146 y Fv(\003)917 1176 y FB(ha)n(ving)e(length)i FA(R)1486 1146 y Fx(2)1523 1176 y FA(=)p FB(\()p FA(K)f FB(log)14 b FA(R)q FB(\))19 b(and)g(heigh)n(t)g FA(R)q FB(,)i(with)f(basis)e(con)n(tained)h(inside)722 1276 y Fy(f)p FA(e)803 1245 y Fv(\003)868 1276 y FB(=)28 b Fy(h)p FA(x;)14 b(y)s Fy(i)28 b(2)h(E)1316 1245 y Fv(\003)1396 1276 y FB(:)41 b FA(x)1507 1288 y Fx(2)1573 1276 y FB(=)27 b FA(y)k FB(=)c(2)h(=)f(1)p FA(=)p FB(2)p Fy(g)p FB(.)44 b(W)-7 b(e)31 b(denote)f(b)n(y)g FA(u)g FB(and)h FA(v)i FB(the)e(dual)722 1375 y(sites)26 b(at)f(the)h(b)r(ottom)g(left)h(and)e (b)r(ottom)h(righ)n(t)f(corners)f(of)i Fy(R)p FB(.)37 b(Then,)26 b(for)f FA(K)31 b FB(large)722 1475 y(enough,)c(there)h (exists)f FA(C)i(<)23 b Fy(1)28 b FB(suc)n(h)f(that)1377 1584 y Fw(X)1332 1747 y Fz(\015)t Fx(:)11 b Fz(u)p Fv(!)p Fz(v)1363 1807 y(\015)t Fv(\032R)1555 1663 y FA(q)1595 1629 y Fv(\003)1592 1683 y Fz(\014)1633 1667 y Fn(\003)1668 1683 y Fz(;h)1727 1667 y Fn(\003)1765 1663 y FB(\()p FA(\015)5 b FB(\))23 b Fy(\025)g FA(R)2052 1629 y Fv(\000)p Fz(C)2232 1584 y Fw(X)2187 1758 y Fz(\015)t Fx(:)11 b Fz(u)p Fv(!)p Fz(v)2410 1663 y FA(q)2450 1629 y Fv(\003)2447 1683 y Fz(\014)2488 1667 y Fn(\003)2523 1683 y Fz(;h)2582 1667 y Fn(\003)2620 1663 y FB(\()p FA(\015)5 b FB(\))14 b FA(:)377 b FB(\(A.17\))p Black 639 2005 a Fy(\017)p Black 41 w FB(\([27],)27 b(\(6.9\))h(and)f(Lemma)h(6.9\))f(F)-7 b(or)27 b(an)n(y)f(v)n(ertices)h FA(x;)14 b(y)26 b Fy(2)d FA(E)5 b FB(,)1470 2119 y Fw(X)1426 2293 y Fz(\015)t Fx(:)11 b Fz(x)p Fv(!)p Fz(y)1648 2198 y FA(q)1688 2164 y Fv(\003)1685 2219 y Fz(\014)1726 2202 y Fn(\003)1761 2219 y Fz(;h)1820 2202 y Fn(\003)1854 2219 y Fz(;E)1930 2198 y FB(\()p FA(\015)5 b FB(\))23 b(=)g Fy(h)p FA(\033)2232 2210 y Fz(x)2274 2198 y FA(\033)2321 2210 y Fz(y)2361 2198 y Fy(i)2393 2210 y Fz(\014)2434 2194 y Fn(\003)2469 2210 y Fz(;h)2528 2194 y Fn(\003)2562 2210 y Fz(;E)2652 2198 y FA(:)471 b FB(\(A.18\))722 2455 y(Moreo)n(v)n(er)1438 2552 y Fw(X)1394 2726 y Fz(\015)t Fx(:)10 b Fz(x)p Fv(!)p Fz(y)1616 2631 y FA(q)1656 2596 y Fv(\003)1653 2651 y Fz(\014)1694 2635 y Fn(\003)1728 2651 y Fz(;h)1787 2635 y Fn(\003)1821 2651 y Fz(;)p Fx(s)p Fz(:)p Fx(i)p Fz(:)1930 2631 y FB(\()p FA(\015)5 b FB(\))23 b(=)g Fy(h)p FA(\033)2232 2643 y Fz(x)2274 2631 y FA(\033)2321 2643 y Fz(y)2361 2631 y Fy(i)2393 2643 y Fz(\014)2434 2627 y Fn(\003)2469 2643 y Fz(;h)2528 2627 y Fn(\003)2562 2643 y Fz(;)p Fx(s)p Fz(:)p Fx(i)p Fz(:)2685 2631 y FA(;)438 b FB(\(A.19\))722 2913 y(and)1542 3035 y Fw(X)1498 3209 y Fz(\015)t Fx(:)10 b Fz(x)p Fv(!)p Fz(y)1720 3114 y FA(q)1760 3080 y Fv(\003)1757 3135 y Fz(\014)1798 3118 y Fn(\003)1832 3135 y Fz(;h)1891 3118 y Fn(\003)1930 3114 y FB(\()p FA(\015)5 b FB(\))23 b(=)g Fy(h)p FA(\033)2232 3126 y Fz(x)2274 3114 y FA(\033)2321 3126 y Fz(y)2361 3114 y Fy(i)2393 3126 y Fz(\014)2434 3110 y Fn(\003)2469 3126 y Fz(;h)2528 3110 y Fn(\003)2580 3114 y FA(;)543 b FB(\(A.20\))3146 3332 y(\(A.21\))722 3508 y(where)29 b Fy(h)14 b(\001)g(i)1079 3520 y Fz(\014)1120 3504 y Fn(\003)1154 3520 y Fz(;h)1213 3504 y Fn(\003)1281 3508 y FB(and)29 b Fy(h)14 b(\001)g(i)1559 3520 y Fz(\014)1600 3504 y Fn(\003)1634 3520 y Fz(;h)1693 3504 y Fn(\003)1728 3520 y Fz(;)p Fx(s)p Fz(:)p Fx(i)p Fz(:)1865 3508 y FB(denote)29 b(exp)r(ectation)g(w.r.t.)41 b(the)29 b(in\014nite)h(and)722 3608 y(semi-in\014nite)e(v)n(olume)f(Gibbs)h(measures.)p Black 639 3771 a Fy(\017)p Black 41 w FB(There)f(exists)h FA(c)23 b(>)f FB(0)27 b(and)h FA(l)1594 3783 y Fx(0)1654 3771 y FA(<)23 b Fy(1)k FB(suc)n(h)h(that,)f(for)h(all)f FA(l)r FB(,)1593 3880 y Fw(X)1624 4044 y Fz(\015)t Fx(:)1577 4107 y Fv(j)p Fz(\015)t Fv(j\025)p Fz(l)1742 3959 y FA(q)1779 3971 y Fz(\014)s(;h;N)1961 3959 y FB(\()p FA(\015)5 b FB(\))24 b Fy(\024)e FA(e)2223 3925 y Fv(\000)p Fz(c)p Fx(\()p Fz(l)p Fv(\000)p Fz(l)2425 3933 y Fm(0)2457 3925 y Fx(\))2501 3959 y FA(:)622 b FB(\(A.22\))639 4309 y Fp(Pro)s(of)26 b(of)34 b FB(\(A.22\))p Fp(.)70 b FB(The)22 b(pro)r(of)g(is)g(similar)g(to)g(that)g(of)g(Lemma)g(5.6)g(in)g([26)o (];)j(w)n(e)c(only)515 4408 y(sk)n(etc)n(h)32 b(it.)52 b(Let)33 b FA(R)h FB(b)r(e)f(some)f(big)h(p)r(ositiv)n(e)f(n)n(um)n(b)r (er.)52 b(W)-7 b(e)33 b(mak)n(e)f(a)g(coarse-graining)d(of)515 4508 y(the)24 b(path)g FA(\015)k FB(on)23 b(the)h(scale)f FA(R)q FB(,)h(i.e.)36 b(w)n(e)23 b(set)h FA(t)1887 4520 y Fx(1)1948 4508 y FB(to)f(b)r(e)h(the)g(left)h(endp)r(oin)n(t)f(of)f FA(\015)5 b FB(,)25 b FA(t)2993 4520 y Fz(k)3057 4508 y FB(to)f(b)r(e)g(the)515 4608 y(\014rst)e(p)r(oin)n(t)g(of)g FA(\015)27 b FB(after)22 b FA(t)1272 4620 y Fz(k)q Fv(\000)p Fx(1)1420 4608 y FB(whic)n(h)g(is)g(outside)g(the)h(square)e(of)h (sidelength)g FA(R)h FB(cen)n(tered)e(on)515 4707 y FA(t)545 4719 y Fz(k)q Fv(\000)p Fx(1)671 4707 y FB(,)31 b(and)f(the)g(pro)r (cedure)g(stops)g(when)g(one)g(reac)n(hes)f(the)h(other)g(endp)r(oin)n (t)h(of)f FA(\015)5 b FB(.)44 b(One)515 4807 y(then)23 b(\014rst)g(sum)g(o)n(v)n(er)f(these)h(sites)f FA(t)1629 4819 y Fx(0)1667 4807 y FA(;)14 b(t)1734 4819 y Fx(1)1771 4807 y FA(;)g(:)g(:)g(:)f(;)h(t)1985 4819 y Fz(L)2058 4807 y FB(\(observing)22 b(that,)i(giv)n(en)e FA(t)2899 4819 y Fz(k)2963 4807 y FB(there)h(are)f(at)515 4907 y(most)e FA(C)6 b(R)22 b FB(c)n(hoices)e(for)g FA(t)1284 4919 y Fz(k)q Fx(+1)1409 4907 y FB(,)i(and)e(that)h(the)h(total)e (length)h(of)f(the)h(piece)g(of)g FA(\015)k FB(b)r(et)n(w)n(een)c(t)n (w)n(o)515 5006 y(consecutiv)n(e)f(p)r(oin)n(ts)h(is)g(at)g(most)g FA(R)1623 4976 y Fx(2)1660 5006 y FB(,)h(so)f(that)g FA(L)i Fy(\025)f FA(l)r(=R)2274 4976 y Fx(2)2310 5006 y FB(\))g(and)f(uses)f(\(A.14\),)j(\(A.18\),)f(and)p Black Black eop end %%Page: 28 28 TeXDict begin 28 27 bop Black 515 232 a Fr(En)n(tropic)22 b(repulsion)g(in)f(external)h(\014eld;)g(v)n(ersion)f(from)g(July)g(3,) f(2003)1118 b FB(28)p Black 515 523 a(the)29 b(upp)r(er)f(b)r(ound)h (in)g(\(A.24\))f(b)r(elo)n(w.)39 b(The)28 b(conclusion)g(follo)n(ws)f (since)h FA(\034)2870 535 y Fz(\014)2944 523 y FB(is)g(uniformly)515 623 y(strictly)f(p)r(ositiv)n(e)g(when)h FA(\014)f(>)c(\014)1532 635 y Fz(c)1566 623 y FB(.)p 1654 623 42 42 v 639 772 a(W)-7 b(e)44 b(also)e(use)h(the)h(follo)n(wing)e(results)h(ab)r(out)g (the)h(asymptotic)f(b)r(eha)n(vior)e(of)j(the)515 872 y(b)r(oundary)26 b(2-p)r(oin)n(t)g(function)i Fy(h)p FA(\033)1577 884 y Fz(x)1619 872 y FA(\033)1666 884 y Fz(y)1706 872 y Fy(i)1738 884 y Fz(\014)1779 868 y Fn(\003)1814 884 y Fz(;h)1873 868 y Fn(\003)1907 884 y Fz(;)p Fx(s)p Fz(:)p Fx(i)p Fz(:)2016 872 y FB(:)36 b(Supp)r(ose)27 b(that)h FA(h)22 b(>)h(h)2786 884 y Fz(w)2840 872 y FB(\()p FA(\014)t FB(\);)28 b(then)f(there)515 971 y(exist)g(constan)n(ts)g FA(K)1150 983 y Fx(1)1214 971 y FB(and)h FA(K)1447 983 y Fx(2)1511 971 y FB(suc)n(h)f(that,)h(for)f(an)n(y)g FA(x;)14 b(y)31 b FB(with)d FA(x)2577 983 y Fx(2)2638 971 y FB(=)22 b FA(y)2766 983 y Fx(2)2826 971 y FB(=)h(1)p FA(=)p FB(2,)583 1154 y FA(K)654 1166 y Fx(1)704 1154 y Fy(j)p FA(x)c Fy(\000)f FA(y)s Fy(j)943 1120 y Fv(\000)p Fx(3)p Fz(=)p Fx(2)1099 1154 y FA(e)1138 1120 y Fv(\000)p Fz(\034)1221 1129 y Fu(\014)1260 1120 y Fx(\()p Fd(e)1320 1128 y Fm(1)1352 1120 y Fx(\))12 b Fv(j)p Fz(x)p Fv(\000)p Fz(y)r Fv(j)1582 1154 y Fy(\025)22 b(h)p FA(\033)1748 1166 y Fz(x)1791 1154 y FA(\033)1838 1166 y Fz(y)1878 1154 y Fy(i)1910 1166 y Fz(\014)1951 1150 y Fn(\003)1986 1166 y Fz(;h)2045 1150 y Fn(\003)2079 1166 y Fz(;)p Fx(s)p Fz(:)p Fx(i)p Fz(:)2211 1154 y Fy(\025)g FA(K)2369 1166 y Fx(2)2420 1154 y Fy(j)p FA(x)d Fy(\000)f FA(y)s Fy(j)2659 1120 y Fv(\000)p Fx(3)p Fz(=)p Fx(2)2815 1154 y FA(e)2854 1120 y Fv(\000)p Fz(\034)2937 1129 y Fu(\014)2975 1120 y Fx(\()p Fd(e)3035 1128 y Fm(1)3068 1120 y Fx(\))11 b Fv(j)p Fz(x)p Fv(\000)p Fz(y)r Fv(j)3288 1154 y FA(;)3146 1254 y FB(\(A.23\))515 1353 y(where)27 b FA(\034)791 1365 y Fz(\014)836 1353 y FB(\()p Fp(e)912 1365 y Fx(1)949 1353 y FB(\))h(is)g(the)g(surface)e(tension)i(in)g(the)g(horizon)n(tal) e(direction.)639 1453 y(W)-7 b(e)37 b(also)e(need)h(the)h(corresp)r (onding)d(result)i(for)g(the)g(bulk)h(2-p)r(oin)n(t.)62 b(There)35 b(exists)515 1553 y FA(K)29 b(<)23 b Fy(1)28 b FB(suc)n(h)f(that,)i(for)e(an)n(y)g FA(h)c(>)g(h)1696 1565 y Fz(w)1750 1553 y FB(\()p FA(\014)t FB(\),)29 b(and)f(an)n(y)f (pair)g(of)h(dual)g(sites)f FA(x;)14 b(y)31 b FB(in)d FA(E)33 b FB(suc)n(h)515 1652 y(that)28 b(the)g(set)592 1835 y Fy(S)642 1847 y Fz(K)706 1835 y FB(\()p FA(x;)14 b(y)s FB(\))24 b(=)e Fy(f)p FA(u)h Fy(2)g Fq(Z)1255 1801 y Fx(2)p Fz(;)p Fv(\003)1383 1835 y FB(:)37 b Fy(k)p FA(x)19 b Fy(\000)f FA(u)p Fy(k)1724 1847 y Fx(2)1778 1835 y FB(+)g Fy(k)p FA(y)j Fy(\000)d FA(u)p Fy(k)2138 1847 y Fx(2)2197 1835 y Fy(\024)23 b(k)p FA(x)18 b Fy(\000)g FA(y)s Fy(k)2561 1847 y Fx(2)2616 1835 y FB(+)g FA(K)i FB(log)14 b Fy(k)p FA(x)k Fy(\000)g FA(y)s Fy(k)3187 1847 y Fx(2)3223 1835 y Fy(g)c FA(;)515 2017 y FB(satis\014es)37 b Fy(S)881 2029 y Fz(K)946 2017 y FB(\()p FA(x;)14 b(y)s FB(\))41 b Fy(\032)g(f)p FA(x)g Fy(2)h FA(E)60 b FB(:)55 b FA(x)1758 2029 y Fx(2)1837 2017 y Fy(\025)40 b FB(3)p FA(=)p FB(2)p Fy(g)p FB(,)g(the)f(follo)n(wing)e(holds:)58 b(There)38 b(exist)515 2117 y(constan)n(ts)26 b FA(K)953 2129 y Fx(1)1018 2117 y FB(and)h FA(K)1250 2129 y Fx(2)1315 2117 y FB(suc)n(h)g(that)h(\([29)o(],)g(Prop)r(osition)e(4.6.1.\))585 2324 y FA(K)656 2336 y Fx(1)706 2324 y Fy(j)p FA(x)19 b Fy(\000)f FA(y)s Fy(j)945 2290 y Fv(\000)p Fx(1)p Fz(=)p Fx(2)1101 2324 y FA(e)1140 2284 y Fv(\000)p Fz(\034)1223 2293 y Fu(\014)1261 2284 y Fx(\()1316 2257 y Fu(x)p Fn(\000)p Fu(y)p 1297 2271 148 3 v 1297 2304 a Fn(j)p Fu(x)p Fn(\000)p Fu(y)q Fn(j)1455 2284 y Fx(\))11 b Fv(j)p Fz(x)p Fv(\000)p Fz(y)r Fv(j)1684 2324 y Fy(\025)23 b(h)p FA(\033)1851 2336 y Fz(x)1893 2324 y FA(\033)1940 2336 y Fz(y)1981 2324 y Fy(i)2013 2336 y Fz(\014)2054 2320 y Fn(\003)2088 2336 y Fz(;h)2147 2320 y Fn(\003)2209 2324 y Fy(\025)f FA(K)2367 2336 y Fx(2)2418 2324 y Fy(j)p FA(x)d Fy(\000)f FA(y)s Fy(j)2657 2290 y Fv(\000)p Fx(1)p Fz(=)p Fx(2)2813 2324 y FA(e)2852 2290 y Fv(\000)p Fz(\034)2935 2299 y Fu(\014)2973 2290 y Fx(\()p Fd(e)3033 2298 y Fm(1)3066 2290 y Fx(\))11 b Fv(j)p Fz(x)p Fv(\000)p Fz(y)r Fv(j)3286 2324 y FA(:)3146 2423 y FB(\(A.24\))639 2523 y(An)37 b(imp)r(ortan)n(t)f(prop)r(ert)n(y)e(of)j(surface)e(tension)h(is)g (that)g(it)g(satis\014es)g(the)g(follo)n(wing)515 2623 y Fj(sharp)26 b(triangle)h(inequalit)n(y)g FB(\([27],)g(Theorem)g (2.1\):)36 b(There)27 b(exists)h FA(\024)23 b(>)f FB(0)27 b(suc)n(h)h(that,)g(for)515 2722 y(an)n(y)f FA(x;)14 b(y)s FB(,)1043 2822 y FA(\034)1079 2834 y Fz(\014)1124 2822 y FB(\()p FA(x)p FB(\))19 b(+)f FA(\034)1373 2834 y Fz(\014)1418 2822 y FB(\()p FA(y)s FB(\))23 b Fy(\025)g FA(\034)1673 2834 y Fz(\014)1718 2822 y FB(\()p FA(x)c FB(+)f FA(y)s FB(\))h(+)f FA(\024)p FB(\()p Fy(j)p FA(x)p Fy(j)h FB(+)f Fy(j)p FA(y)s Fy(j)g(\000)g(j)p FA(x)h FB(+)f FA(y)s Fy(j)p FB(\))c FA(:)295 b FB(\(A.25\))639 2971 y(Finally)-7 b(,)41 b(w)n(e)d(also)e(need)j(the)f(follo)n(wing)f (estimate)h(on)g(the)g(relaxation)e(of)i(correla-)515 3071 y(tion)28 b(functions)h(\([10)o(]\):)39 b(Supp)r(ose)28 b(that)h FA(h)f FB(and)g FA(\025)h FB(are)e(non-negativ)n(e;)g(then)i (there)f(exists)515 3171 y FA(C)6 b FB(\()p FA(\014)t FB(\))24 b FA(>)f FB(0)k(and)g FA(K)i(<)22 b Fy(1)28 b FB(suc)n(h)f(that,)h(for)f(an)n(y)g(\003)2067 3183 y Fx(1)2104 3171 y FA(;)14 b FB(\003)2199 3183 y Fx(2)2259 3171 y Fy(\032)23 b Fq(Z)2402 3140 y Fx(2)2467 3171 y FB(and)k FA(A)d Fy(\032)e FB(\003)2859 3183 y Fx(1)2915 3171 y Fy([)c FB(\003)3046 3183 y Fx(2)3083 3171 y FB(,)773 3370 y Fy(jh)p FA(\033)875 3382 y Fz(A)930 3370 y Fy(i)962 3382 y Fx(+)p Fz(;\014)s(;\025;h;)p Fx(\003)1257 3390 y Fm(1)1312 3370 y Fy(\000)g(h)p FA(\033)1474 3382 y Fz(A)1529 3370 y Fy(i)1561 3382 y Fx(+)p Fz(;\014)s(;\025;h;)p Fx(\003)1856 3390 y Fm(2)1891 3370 y Fy(j)24 b(\024)e FA(K)2209 3291 y Fw(X)2209 3469 y Fz(t)p Fv(2)p Fz(A)2116 3530 y(t)2141 3505 y Fn(0)2163 3530 y Fv(2)p Fx(\003)2253 3538 y Fm(1)2286 3530 y Fv(4)p Fx(\003)2390 3538 y Fm(2)2436 3370 y FA(e)2475 3336 y Fv(\000)p Fz(C)t Fx(\()p Fz(\014)s Fx(\))10 b Fv(j)p Fz(t)2727 3311 y Fn(0)2750 3336 y Fv(\000)p Fz(t)p Fv(j)2864 3370 y FA(;)259 b FB(\(A.26\))515 3703 y(where)27 b FA(\033)802 3715 y Fz(A)879 3703 y FB(=)967 3641 y Fw(Q)1045 3728 y Fz(x)p Fv(2)p Fz(A)1196 3703 y FA(\033)1243 3715 y Fz(x)1285 3703 y FB(.)515 3978 y FD(References)p Black 556 4160 a FB([1])p Black 41 w(D.)i(B.)f(Abraham.)37 b(Solv)-5 b(able)28 b(mo)r(del)g(with)h(a)e (roughening)g(transition)g(for)h(a)f(planar)685 4259 y(Ising)g(ferromagnet.)36 b Fo(Phys.)31 b(R)l(ev.)f(L)l(ett.)p FB(,)d(44\(18\):1165{1168,)22 b(1980.)p Black 556 4425 a([2])p Black 41 w(D.)27 b(Bertacc)n(hi)d(and)i(G.)g(Giacomin.)34 b(W)-7 b(all)26 b(repulsion)f(and)h(m)n(utual)f(in)n(terface)h(repul-) 685 4525 y(sion:)37 b(an)27 b(harmonic)g(crystal)f(mo)r(del)i(in)g (high)f(dimension.)37 b Fo(Pr)l(eprint)30 b(\(2002\))p FB(.)p Black 556 4691 a([3])p Black 41 w(D.)20 b(Bertacc)n(hi)d(and)i (G.)g(Giacomin.)j(Enhanced)d(in)n(terface)f(repulsion)g(from)g(quenc)n (hed)685 4791 y(hard-w)n(all)43 b(randomness.)85 b Fo(Pr)l(ob)l(ab.)47 b(The)l(ory)f(R)l(elate)l(d)g(Fields)p FB(,)k(124\(4\):487{516,)685 4890 y(2002.)p Black Black eop end %%Page: 29 29 TeXDict begin 29 28 bop Black 515 232 a Fr(En)n(tropic)22 b(repulsion)g(in)f(external)h(\014eld;)g(v)n(ersion)f(from)g(July)g(3,) f(2003)1118 b FB(29)p Black Black 556 523 a([4])p Black 41 w(E.)24 b(Bolthausen)e(and)i(D.)g(Brydges.)29 b(Lo)r(calization)22 b(and)h(deca)n(y)g(of)g(correlations)e(for)i(a)685 623 y(pinned)28 b(lattice)f(free)g(\014eld)g(in)g(dimension)g(t)n(w)n(o.)35 b(In)27 b Fo(State)i(of)h(the)f(art)g(in)h(pr)l(ob)l(ability)685 722 y(and)40 b(statistics)g(\(L)l(eiden,)j(1999\))p FB(,)f(v)n(olume)c (36)f(of)h Fo(IMS)i(L)l(e)l(ctur)l(e)e(Notes)i(Mono)l(gr.)685 822 y(Ser.)p FB(,)28 b(pages)f(134{149.)d(Inst.)k(Math.)g(Statist.,)g (Beac)n(h)n(w)n(o)r(o)r(d,)e(OH,)h(2001.)p Black 556 983 a([5])p Black 41 w(E.)k(Bolthausen,)g(J.-D.)g(Deusc)n(hel,)h(and)f (G.)g(Giacomin.)46 b(En)n(tropic)30 b(repulsion)g(and)685 1082 y(the)43 b(maxim)n(um)f(of)g(the)g(t)n(w)n(o-dimensional)f (harmonic)g(crystal.)79 b Fo(A)n(nn.)42 b(Pr)l(ob)l(ab.)p FB(,)685 1182 y(29\(4\):1670{1692,)23 b(2001.)p Black 556 1343 a([6])p Black 41 w(E.)28 b(Bolthausen,)g(J.-D.)h(Deusc)n(hel,) f(and)g(O.)h(Zeitouni.)39 b(En)n(tropic)27 b(repulsion)g(of)i(the)685 1443 y(lattice)f(free)f(\014eld.)38 b Fo(Comm.)30 b(Math.)h(Phys.)p FB(,)f(170\(2\):417{443,)23 b(1995.)p Black 556 1604 a([7])p Black 41 w(E.)40 b(Bolthausen,)j(J.-D.)d(Deusc)n(hel,)j(and)d (O.)g(Zeitouni.)74 b(Absence)40 b(of)g(a)g(w)n(etting)685 1703 y(transition)25 b(for)h(a)f(pinned)h(harmonic)f(crystal)g(in)h (dimensions)f(three)h(and)f(larger.)32 b Fo(J.)685 1803 y(Math.)23 b(Phys.)p FB(,)g(41\(3\):1211{1223,)15 b(2000.)21 b(Probabilistic)c(tec)n(hniques)i(in)g(equilibrium)685 1902 y(and)28 b(nonequilibrium)f(statistical)g(ph)n(ysics.)p Black 556 2063 a([8])p Black 41 w(E.)j(Bolthausen)g(and)g(Y.)h(V)-7 b(elenik.)46 b(Critical)29 b(b)r(eha)n(vior)g(of)i(the)g(massless)e (free)h(\014eld)685 2163 y(at)e(the)g(depinning)g(transition.)36 b Fo(Comm.)31 b(Math.)g(Phys.)p FB(,)e(223\(1\):161{203,)23 b(2001.)p Black 556 2324 a([9])p Black 41 w(J.)38 b(Bricmon)n(t,)i(A.)f (El)e(Mellouki,)k(and)d(J.)g(F)-7 b(r\177)-42 b(ohlic)n(h.)67 b(Random)38 b(surfaces)e(in)j(sta-)685 2424 y(tistical)e(mec)n(hanics:) 55 b(roughening,)39 b(rounding,)f(w)n(etting,)p FA(:)14 b(:)g(:)g FB(.)65 b Fo(J.)38 b(Statist.)g(Phys.)p FB(,)685 2523 y(42\(5-6\):743{798,)23 b(1986.)p Black 515 2684 a([10])p Black 40 w(J.)32 b(Bricmon)n(t,)f(J.)g(L.)h(Leb)r(o)n(witz,)g (and)f(C.)h(E.)f(P\014ster.)47 b(On)32 b(the)f(lo)r(cal)g(structure)g (of)685 2784 y(the)h(phase)f(separation)e(line)j(in)f(the)h(t)n(w)n (o-dimensional)d(Ising)i(system.)47 b Fo(J.)33 b(Statist.)685 2883 y(Phys.)p FB(,)d(26\(2\):313{332,)23 b(1981.)p Black 515 3044 a([11])p Black 40 w(M.)g(Campanino,)f(D.)g(Io\013e,)h(and)f (Y.)h(V)-7 b(elenik.)27 b(Ornstein-Zernik)n(e)20 b(theory)h(for)h (\014nite-)685 3144 y(range)g(ising)h(mo)r(dels)g(ab)r(o)n(v)n(e)f FA(T)1652 3156 y Fx(c)1685 3144 y FB(.)30 b Fo(Pr)l(ob)l(ab.)d(The)l (ory)g(R)l(elat.)f(Fields)p FB(,)g(125\(3\):305{349,)685 3244 y(2003.)p Black 515 3405 a([12])p Black 40 w(P)-7 b(.)25 b(Caputo)g(and)h(Y.)f(V)-7 b(elenik.)34 b(A)26 b(note)f(on)g(w)n(etting)g(transition)g(for)g(gradien)n(t)f(\014elds.) 685 3504 y Fo(Sto)l(chastic)31 b(Pr)l(o)l(c)l(ess.)f(Appl.)p FB(,)f(87\(1\):107{113,)24 b(2000.)p Black 515 3665 a([13])p Black 40 w(F.)36 b(Cesi)f(and)g(F.)g(Martinelli.)60 b(On)35 b(the)g(la)n(y)n(ering)e(transition)i(of)g(an)g(SOS)g(surface)685 3765 y(in)n(teracting)41 b(with)h(a)e(w)n(all.)h(I.)h(Equilibrium)f (results.)77 b Fo(J.)42 b(Statist.)g(Phys.)p FB(,)47 b(82\(3-)685 3864 y(4\):823{913,)25 b(1996.)p Black 515 4025 a([14])p Black 40 w(J.-D.)44 b(Deusc)n(hel.)83 b(En)n(tropic)42 b(repulsion)h(of)g(the)h(lattice)f(free)g(\014eld.)h(I)r(I.)f(The)h(0-) 685 4125 y(b)r(oundary)27 b(case.)36 b Fo(Comm.)31 b(Math.)g(Phys.)p FB(,)e(181\(3\):647{665,)23 b(1996.)p Black 515 4286 a([15])p Black 40 w(J.-D.)41 b(Deusc)n(hel)f(and)g(G.)h(Giacomin.)75 b(En)n(tropic)39 b(repulsion)h(for)g(the)h(free)f(\014eld:)685 4385 y(path)n(wise)31 b(c)n(haracterization)d(in)j FA(d)d Fy(\025)g FB(3.)46 b Fo(Comm.)34 b(Math.)g(Phys.)p FB(,)f (206\(2\):447{462,)685 4485 y(1999.)p Black 515 4646 a([16])p Black 40 w(J.-D.)k(Deusc)n(hel)f(and)g(G.)g(Giacomin.)62 b(En)n(tropic)35 b(repulsion)g(for)h(massless)f(\014elds.)685 4746 y Fo(Sto)l(chastic)c(Pr)l(o)l(c)l(ess.)f(Appl.)p FB(,)f(89\(2\):333{354,)24 b(2000.)p Black 515 4907 a([17])p Black 40 w(J.-D.)35 b(Deusc)n(hel)g(and)g(Y.)g(V)-7 b(elenik.)60 b(Non-Gaussian)33 b(surface)h(pinned)i(b)n(y)f(a)f(w)n(eak)685 5006 y(p)r(oten)n(tial.)j Fo(Pr)l(ob)l(ab.)31 b(The)l(ory)h(R)l(elate)l (d)d(Fields)p FB(,)h(116\(3\):359{377,)23 b(2000.)p Black Black eop end %%Page: 30 30 TeXDict begin 30 29 bop Black 515 232 a Fr(En)n(tropic)22 b(repulsion)g(in)f(external)h(\014eld;)g(v)n(ersion)f(from)g(July)g(3,) f(2003)1118 b FB(30)p Black Black 515 523 a([18])p Black 40 w(E.)33 b(I.)g(Dinaburg)f(and)h(A.)g(E.)f(Mazel.)52 b(La)n(y)n(ering)31 b(transition)h(in)h(SOS)g(mo)r(del)g(with)685 623 y(external)27 b(magnetic)g(\014eld.)37 b Fo(J.)30 b(Statist.)g(Phys.)p FB(,)f(74\(3-4\):533{563,)22 b(1994.)p Black 515 789 a([19])p Black 40 w(R.)28 b(L.)g(Dobrushin.)37 b(A)28 b(statistical)f(b)r(eha)n(vior)g(of)g(shap)r(es)h(of)f(b)r (oundaries)g(of)h(phases.)685 888 y(In)i(R.)f(Kotec)n(k)q(\023)-43 b(y,)28 b(editor,)h Fo(Phase)j(Tr)l(ansitions:)42 b(Mathematics,)34 b(Physics,)f(Biolo)l(gy,)685 988 y(.)13 b(.)g(.)g FB(,)29 b(pages)d(60{70.)f(W)-7 b(orld)28 b(Scien)n(ti\014c,)g(Singap)r(ore,)e (1993.)p Black 515 1154 a([20])p Black 40 w(F.)e(Dunlop,)g(J.)f (Magnen,)h(V.)g(Riv)-5 b(asseau,)23 b(and)g(P)-7 b(.)23 b(Ro)r(c)n(he.)29 b(Pinning)23 b(of)g(an)g(in)n(terface)685 1254 y(b)n(y)28 b(a)f(w)n(eak)f(p)r(oten)n(tial.)37 b Fo(J.)30 b(Statist.)f(Phys.)p FB(,)h(66\(1-2\):71{98,)23 b(1992.)p Black 515 1420 a([21])p Black 40 w(J.)i(F)-7 b(r\177)-42 b(ohlic)n(h)24 b(and)g(C.-E.)g(P\014ster.)31 b(Semi-in\014nite)25 b(Ising)f(mo)r(del.)h(I.)g(Thermo)r(dynamic)685 1519 y(functions)33 b(and)e(phase)h(diagram)e(in)i(absence)g(of)f (magnetic)h(\014eld.)50 b Fo(Comm.)35 b(Math.)685 1619 y(Phys.)p FB(,)30 b(109\(3\):493{523,)23 b(1987.)p Black 515 1785 a([22])p Black 40 w(O.)29 b(Hryniv)g(and)g(Y.)g(V)-7 b(elenik.)42 b(Univ)n(ersalit)n(y)27 b(of)j(critical)e(b)r(eha)n(viour) g(for)g(a)h(class)f(of)685 1885 y(recurren)n(t)f(random)f(w)n(alks.)36 b(Preprin)n(t)26 b(\(2003\).)p Black 515 2051 a([23])p Black 40 w(D.)21 b(Io\013e)e(and)g(Y.)h(V)-7 b(elenik.)24 b(A)c(note)g(on)f(the)h(deca)n(y)f(of)g(correlations)f(under)h FA(\016)s FB(-pinning.)685 2150 y Fo(Pr)l(ob)l(ab.)32 b(The)l(ory)f(R)l(elate)l(d)f(Fields)p FB(,)f(116\(3\):379{389,)23 b(2000.)p Black 515 2316 a([24])p Black 40 w(Y.)43 b(Isozaki)e(and)h (N.)h(Y)-7 b(oshida.)80 b(W)-7 b(eakly)42 b(pinned)g(random)g(w)n(alk)f (on)h(the)h(w)n(all:)685 2416 y(path)n(wise)36 b(descriptions)g(of)g (the)g(phase)g(transition.)62 b Fo(Sto)l(chastic)38 b(Pr)l(o)l(c)l (ess.)h(Appl.)p FB(,)685 2516 y(96\(2\):261{284,)24 b(2001.)p Black 515 2682 a([25])p Black 40 w(J.)d(L.)g(Leb)r(o)n(witz)g(and)g(A.) h(E.)f(Mazel.)k(A)d(remark)d(on)i(the)h(lo)n(w-temp)r(erature)d(b)r (eha)n(vior)685 2781 y(of)25 b(the)h(SOS)f(in)n(terface)f(in)h (half-space.)32 b Fo(J.)27 b(Statist.)g(Phys.)p FB(,)g (84\(3-4\):379{397,)21 b(1996.)p Black 515 2947 a([26])p Black 40 w(C.-E.)27 b(P\014ster)g(and)h(Y.)g(V)-7 b(elenik.)38 b(Large)26 b(deviations)h(and)g(con)n(tin)n(uum)h(limit)h(in)f(the)685 3047 y(2D)g(Ising)f(mo)r(del.)37 b Fo(Pr)l(ob)l(ab.)31 b(The)l(ory)h(R)l(elate)l(d)d(Fields)p FB(,)h(109\(4\):435{506,)23 b(1997.)p Black 515 3213 a([27])p Black 40 w(C.-E.)28 b(P\014ster)g(and)h(Y.)g(V)-7 b(elenik.)40 b(In)n(terface,)29 b(surface)f(tension)g(and)h(reen)n(tran)n(t)e(pin-)685 3313 y(ning)21 b(transition)e(in)i(the)g(2D)f(Ising)g(mo)r(del.)26 b Fo(Comm.)e(Math.)g(Phys.)p FB(,)g(204\(2\):269{312,)685 3412 y(1999.)p Black 515 3578 a([28])p Black 40 w(R.)35 b(H.)g(Sc)n(honmann)f(and)g(S.)h(B.)f(Shlosman.)56 b(Constrained)34 b(v)-5 b(ariational)33 b(problem)685 3678 y(with)k(applications)d(to)i (the)g(Ising)f(mo)r(del.)61 b Fo(J.)37 b(Statist.)g(Phys.)p FB(,)i(83\(5-6\):867{905,)685 3778 y(1996.)p Black 515 3944 a([29])p Black 40 w(Y.)29 b(V)-7 b(elenik.)38 b Fo(Phase)32 b(sep)l(ar)l(ation)f(as)f(a)h(lar)l(ge)g(deviations)h(pr)l (oblem:)40 b(a)31 b(micr)l(osc)l(opic)685 4043 y(derivation)25 b(of)e(surfac)l(e)g(thermo)l(dynamics)g(in)g(some)g(2D)f(spin)h (systems)p FB(.)g(PhD)d(thesis,)685 4143 y(E.P)-7 b(.F.L.,)28 b(1997.)p Black Black eop end %%Trailer userdict /end-hook known{end-hook}if %%EOF ---------------0307030342736--