Нашли опечатку? Выделите ее мышкой и нажмите Ctrl+Enter
Название: Advanced Statistical Properties of Dispersing Billiards
Автор: Chernov N.
Journal of Statistical Physics, Vol. 122, No. 6, March 2006, p. 1061-1094.
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.