Advanced Statistical Properties of Dispersing Billiards
 N. Chernov
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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.
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 Title
 Advanced Statistical Properties of Dispersing Billiards
 Journal

Journal of Statistical Physics
Volume 122, Issue 6 , pp 10611094
 Cover Date
 20060301
 DOI
 10.1007/s1095500690368
 Print ISSN
 00224715
 Online ISSN
 15729613
 Publisher
 Springer US
 Additional Links
 Topics
 Keywords

 Sinai billiards
 decay of correlations
 central limit theorem
 invariance principle
 law of iterated logarithms
 Industry Sectors
 Authors

 N. Chernov ^{(1)}
 Author Affiliations

 1. Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL, 35294, UK