Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Characterization of weak convergence of Birkhoff sums for Gibbs-Markov
  maps   We investigate limit theorems for Birkhoff sums of locally H\"older 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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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: physics
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The categories of this paper are: hep-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: econ