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Israel Journal of Mathematics

, Volume 139, Issue 1, pp 29–65 | Cite as

Sharp polynomial estimates for the decay of correlations

  • Sébastien Gouëzel
Article

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.

Keywords

Central Limit Theorem Fourier Coefficient Transfer Operator Banach Algebra Spectral Projection 
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Copyright information

© Hebrew University 2004

Authors and Affiliations

  1. 1.Laboratoire de mathématiquesUniversité Paris-SudOrsayFrance

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