N. Chernov
Advanced statistical properties of dispersing billiards
(136K, LaTeX)

ABSTRACT.  A new approach to statistical properties of hyperbolic dynamical 
systems emerged recently; it was introduced by L.-S.~Young and 
modified by D.~Dolgopyat. It is based on coupling method borrowed 
from probability theory. We apply it here to one of the most 
physically interesting models -- Sinai billiards. It allows us to 
derive a series of new results, as well as make significant 
improvements in the existing results. First we establish sharp 
bounds on correlations (including multiple correlations). Then we 
use our correlation bounds to obtain the central limit theorem 
(CLT), the almost sure invariance principle (ASIP), the law of 
iterated logarithms, and integral tests.