 0670 Fern ndez R.
 Gibbsianness and nonGibbsianness in lattice random fields
(198K, LATeX 2e)
Mar 15, 06

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Abstract. These are the notes for a minicourse at
the Les Houches summer school
\emph{Mathematical Statistical Physics}
(July 4 July 29, 2005)
The main topics of the course are the following:
(i) Review, with some detail, of the topological and
measuretheoretical notions needed to define
Gibbs measures. (ii) The notion of specification and discussion of
properties related to Gibbsianness (nonnullness, directional
quasilocality, continuity\ldots) (iii) Kozlov's theorem relating
Gibbsianness with nonnullness and quasilocality: (hopefully)
pedagogical presentation of the proof and discussion of its
consequences for weaker forms of Gibbsianness. (iv) NonGibbsianness
of measures obtained via linear transformations: mechnisms
and strategy of proofs. (v) Three benchmark examples of
nonGibbsianness: renormalization maps, spinflip evolutions and
disordered models.
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