A Strong Pair Correlation Bound Implies the CLT for Sinai Billiards

@article{Stenlund2009ASP,
title={A Strong Pair Correlation Bound Implies the CLT for Sinai Billiards},
author={Mikko Stenlund},
journal={Journal of Statistical Physics},
year={2009},
volume={140},
pages={154-169}
}
• Mikko Stenlund
• Published 31 July 2009
• Mathematics, Physics
• Journal of Statistical Physics
We investigate the possibility of proving the Central Limit Theorem (CLT) for Dynamical Systems using only information on pair correlations. A strong bound on multiple correlations is known to imply the CLT (Chernov and Markarian in Chaotic Billiards, 2006). In Chernov’s paper (J. Stat. Phys. 122(6), 2006), 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…
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