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Berry-Esseen theorem and local limit theorem for non uniformly expanding maps

Sebastien Gouezel
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Abstract

We prove that, in Young towers with sufficiently small tails, the speed in the central limit theorem is O(1/\sqrt{n}), and the local limit theorem holds. This implies the same results for many non uniformly expanding dynamical systems, namely those for which a tower with sufficiently fast returns can be constructed.

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Sebastien Gouezel. 2004-12-13. Berry-Esseen theorem and local limit theorem for non uniformly expanding maps. https://arxiv.org/abs/math/0310391

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