Large deviation principles for countable markov shifts

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Abstract

We establish the large deviation principle for a topological Markov shift over infinite alphabet which satisfies strong connectivity assumptions called “finite irreducibility” or “finite primitiveness”. More precisely, we assume the existence of a Gibbs state for a potential φ in the sense of Bowen, and prove the level-2 large deviation principles for the distribution of empirical means under the Gibbs state, as well as that of weighted periodic points and iterated preimages. The rate function is written with the pressure and the free energy associated with the potential φ.

Original languageEnglish
Pages (from-to)7831-7855
Number of pages25
JournalTransactions of the American Mathematical Society
Volume372
Issue number11
DOIs
Publication statusPublished - 2019 Dec 1

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ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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