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Minimal distance between random orbits

Abstract : We study the minimal distance between two orbit segments of length n, in a random dynamical system with sufficiently good mixing properties. This problem has already been solved in non-random dynamical system, and on average in random dynamical systems (the so-called annealed version of the problem): it is known that the asymptotic behavior for this question is given by a dimension-like quantity associated to the invariant measure, called its correlation dimension (or Rényi entropy). We study the analogous quenched question, and show that the asymptotic behavior is more involved: two correlation dimensions show up, giving rise to a non-smooth behavior of the associated asymptotic exponent.
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Pré-publication, Document de travail
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https://hal.archives-ouvertes.fr/hal-03788538
Contributeur : Sebastien Gouezel Connectez-vous pour contacter le contributeur
Soumis le : lundi 26 septembre 2022 - 17:19:19
Dernière modification le : mercredi 28 septembre 2022 - 05:38:12

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  • HAL Id : hal-03788538, version 1
  • ARXIV : 2209.13240

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Sébastien Gouëzel, Jérôme Rousseau, Manuel Stadlbauer. Minimal distance between random orbits. {date}. ⟨hal-03788538⟩

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