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A Stretched Exponential Bound on Time Correlations for Billiard Flows

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Abstract

We construct Markov approximations to the billiard flows and establish a stretched exponential bound on time-correlation functions for planar periodic Lorentz gases (also known as Sinai billiards). Precisely, we show that for any (generalized) Hölder continuous functions F,G on the phase space of the flow the time correlation function is bounded by const⋅ \(e^{-a\sqrt{|t|}}\), here t ∊ ℝ is the (continuous) time and a > 0.

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

    N. Chernov

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  1. N. Chernov
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Chernov, N. A Stretched Exponential Bound on Time Correlations for Billiard Flows. J Stat Phys 127, 21–50 (2007). https://doi.org/10.1007/s10955-007-9293-1

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