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

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 som...

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Bibliographic Details
Published in:Lobachevskii journal of mathematics 2022-07, Vol.43 (7), p.1633-1640
Main Author: Gurevich, B. M.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Formalism
Geometry
Markov chains
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
Thermodynamics
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Summary: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.
ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080222100134