caa a22 4500 467892407 CHVBK 20180406152752.0 cr unu---uuuuu 170328e20060301xx s 000 0 eng 10.1007/s10955-006-9036-8 doi (NATIONALLICENCE)springer-10.1007/s10955-006-9036-8 Chernov N. Department of Mathematics, University of Alabama at Birmingham, 35294, Birmingham, AL, UK aut Advanced Statistical Properties of Dispersing Billiards [Elektronische Daten] [N. Chernov] 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. Springer Science + Business Media, Inc., 2006 Sinai billiards nationallicence decay of correlations nationallicence central limit theorem nationallicence invariance principle nationallicence law of iterated logarithms nationallicence Journal of Statistical Physics Springer US; http://www.springer-ny.com 122/6(2006-03-01), 1061-1094 0022-4715 122:6<1061 2006 122 10955 https://doi.org/10.1007/s10955-006-9036-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-006-9036-8 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Chernov N. Department of Mathematics, University of Alabama at Birmingham, 35294, Birmingham, AL, UK aut NATIONALLICENCE 773 0- Journal of Statistical Physics Springer US; http://www.springer-ny.com 122/6(2006-03-01), 1061-1094 0022-4715 122:6<1061 2006 122 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer