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Non-uniform Specification and Large Deviations for Weak Gibbs Measures

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Abstract

We establish bounds for the measure of deviation sets associated to continuous observables with respect to not necessarily invariant weak Gibbs measures. Under some mild assumptions, we obtain upper and lower bounds for the measure of deviation sets of some non-uniformly expanding maps, including quadratic maps and robust multidimensional non-uniformly expanding local diffeomorphisms. For that purpose, a measure theoretical weak form of specification is introduced and proved to hold for the robust classes of multidimensional non-uniformly expanding local diffeomorphisms and Viana maps.

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  1. Departamento de Matemática, Universidade Federal da Bahia, Av. Ademar de Barros s/n, 40170-110, Salvador, Brazil

    Paulo Varandas

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  1. Paulo Varandas
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Varandas, P. Non-uniform Specification and Large Deviations for Weak Gibbs Measures. J Stat Phys 146, 330–358 (2012). https://doi.org/10.1007/s10955-011-0392-7

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  • DOI: https://doi.org/10.1007/s10955-011-0392-7

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