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arXiv · 0809.0656

Characterization of weak convergence of Birkhoff sums for Gibbs-Markov maps

Sebastien Gouezel
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Abstract

We investigate limit theorems for Birkhoff sums of locally Hölder functions under the iteration of Gibbs-Markov maps. Aaronson and Denker have given sufficient conditions to have limit theorems in this setting. We show that these conditions are also necessary: there is no exotic limit theorem for Gibbs-Markov maps. Our proofs, valid under very weak regularity assumptions, involve weak perturbation theory and interpolation spaces. For L^2 observables, we also obtain necessary and sufficient conditions to control the speed of convergence in the central limit theorem.

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Sebastien Gouezel. 2009-07-08. Characterization of weak convergence of Birkhoff sums for Gibbs-Markov maps. https://arxiv.org/abs/0809.0656

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