A Strong Pair Correlation Bound Implies the Clt for Sinai Billiards
نویسنده
چکیده
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 Hölder 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. Acknowledgement. The author is partially supported by a fellowship from the Academy of Finland. He is grateful to Lai-Sang Young for her encouragement.
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