Sharp polynomial estimates for the decay of correlations

Details Sharp polynomial estimates for the decay of correlations Sharp polynomial estimates for the decay of correlations

2002-02-15

arxiv.org/abs/math/0202147v1

Mathematics

Dynamical Systems

33 pages

Scientific paper

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+\alpha) with 1/2 < \alpha < 1. The method is based on a general result on renewal sequences of operator, and gives an asymptotic estimate up to any precision of such operators.

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