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Some Old and New Problems in Thermodynamic Formalism of Infinite State Markov Chains

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Abstract

A review of some results and open problems in Thermodynamic Formalism of Infinite Alphabet Markov Shifts (TFIAMS) is presented. The authors of main works, thanks to which this mathematical field has appeared, are mentioned, and specific aims of these authors are described. Then basic notions and some basic results of TFIAMS are recalled. In conclusion, a few generalizations and modifications of these results are stated in form of hypotheses.

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Authors and Affiliations

  1. Lomonosov Moscow State University, 119991, Moscow, Russia

    B. M. Gurevich

  2. Kharkevich Institute for Information Transmission Problems of the Russian Academy of Sciences, 127051, Moscow, Russia

    B. M. Gurevich

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  1. B. M. Gurevich
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Correspondence to B. M. Gurevich.

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(Submitted by E. A. Turilova)

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Gurevich, B.M. Some Old and New Problems in Thermodynamic Formalism of Infinite State Markov Chains. Lobachevskii J Math 43, 1633–1640 (2022). https://doi.org/10.1134/S1995080222100134

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  • DOI: https://doi.org/10.1134/S1995080222100134

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