Uniqueness of Minimizer for Countable Markov Shifts and Equidistribution of Periodic Points

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Abstract

For a finitely irreducible countable Markov shift and a potential with summable variations, we provide a condition on the associated pressure function which ensures that Bowen’s Gibbs state, the equilibrium state, and the minimizer of the level-2 large deviations rate function are all unique and they coincide. From this, we deduce that the set of periodic points weighted with the potential equidistributes with respect to the Gibbs-equilibrium state as the periods tend to infinity. Applications are given to the Gauss map, and the Bowen-Series map associated with a finitely generated free Fuchsian group with parabolic elements.

Original languageEnglish
Pages (from-to)2415-2431
Number of pages17
JournalJournal of Statistical Physics
Volume181
Issue number6
DOIs
Publication statusPublished - 2020 Dec

Keywords

  • Countable Markov shift
  • Gibbs-equilibrium state
  • Large deviation principle
  • Minimizer

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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