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Optimal Concentration Inequalities for Dynamical Systems

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Abstract

For dynamical systems modeled by a Young tower with exponential tails, we prove an exponential concentration inequality for all separately Lipschitz observables of n variables. When tails are polynomial, we prove polynomial concentration inequalities. Those inequalities are optimal. We give some applications of such inequalities to specific systems and specific observables.

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Authors and Affiliations

  1. CPHT, CNRS UMR 7644, Ecole Polytechnique, 91128, Palaiseau Cedex, France

    Jean-René Chazottes

  2. IRMAR, CNRS UMR 6625, Université de Rennes 1, 35042, Rennes, France

    Sébastien Gouëzel

Authors
  1. Jean-René Chazottes
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  2. Sébastien Gouëzel
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Correspondence to Sébastien Gouëzel.

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Communicated by G. Gallavotti

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Chazottes, JR., Gouëzel, S. Optimal Concentration Inequalities for Dynamical Systems. Commun. Math. Phys. 316, 843–889 (2012). https://doi.org/10.1007/s00220-012-1596-7

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  • DOI: https://doi.org/10.1007/s00220-012-1596-7

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