A strong pair correlation bound implies the CLT for Sinai Billiards

Details A strong pair correlation bound implies the CLT for Sinai Billiards A strong pair correlation bound implies the CLT for Sinai Billiards

2009-07-31

arxiv.org/abs/0908.0027v1

J Stat Phys (2010) 140: 154-169

Mathematics

Dynamical Systems

13 pages

Scientific paper

10.1007/s10955-010-9987-7

For Dynamical Systems, a strong bound on multiple correlations implies the Central Limit Theorem (CLT) [ChMa]. In Chernov's paper [Ch2], such a bound is derived for dynamically Holder continuous observables of dispersing Billiards. Here we weaken the regularity assumption and subsequently show that the bound on multiple correlations follows directly from the bound on pair correlations. Thus, a strong bound on pair correlations alone implies the CLT, for a wider class of observables. The result is extended to Anosov diffeomorphisms in any dimension.

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