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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- Advanced Statistical Properties of Dispersing Billiards
Journal of Statistical Physics
Volume 122, Issue 6 , pp 1061-1094
- Cover Date
- Print ISSN
- Online ISSN
- Springer US
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- Sinai billiards
- decay of correlations
- central limit theorem
- invariance principle
- law of iterated logarithms
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- N. Chernov (1)
- Author Affiliations
- 1. Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL, 35294, UK