Characterization of weak convergence of Birkhoff sums for Gibbs-Markov maps |
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Authors: | Sébastien Gouëzel |
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Institution: | 1.IRMAR, CNRS UMR 6625,Université de Rennes 1,Rennes,France |
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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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