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Sharp polynomial estimates for the decay of correlations

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Abstract

We generalize a method developed by Sarig to obtain polynomial lower bounds for correlation functions for maps with a countable Markov partition. A consequence is that LS Young’s estimates on towers are always optimal. Moreover, we show that, for functions with zero average, the decay rate is better, gaining a factor 1/n. This implies a Central Limit Theorem in contexts where it was not expected, e.g.,x+Cx 1+α with 1/2⩽α<1. The method is based on a general result on renewal sequences of operators, and gives an asymptotic estimate up to any precision of such operators.

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  1. Laboratoire de mathématiques, Université Paris-Sud, bâtiment 425, 91405, Orsay, France

    Sébastien Gouëzel

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  1. Sébastien Gouëzel
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Correspondence to Sébastien Gouëzel.

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Gouëzel, S. Sharp polynomial estimates for the decay of correlations. Isr. J. Math. 139, 29–65 (2004). https://doi.org/10.1007/BF02787541

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  • DOI: https://doi.org/10.1007/BF02787541

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