On the work of Sarig on countable Markov chains and thermodynamic formalism

Yakov Pesin

doi:10.3934/jmd.2014.8.1

Article Contents

2014, Volume 8, Issue 1: 1-14. Doi: 10.3934/jmd.2014.8.1 open access

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On the work of Sarig on countable Markov chains and thermodynamic formalism (Brin Prize article)

Yakov Pesin^1,

1.
Department of Mathematics, McAllister Building, Pennsylvania State University, University Park, PA 16802

Published: June 2014

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Abstract

The paper is a nontechnical survey and is aimed to illustrate Sarig'sprofound contributions to statistical physics and in particular,thermodynamic formalism for countable Markov shifts. I will discusssome of Sarig's work on characterization of existence of Gibbsmeasures, existence and uniqueness of equilibrium states as well asphase transitions for Markov shifts on a countable set of states.

Keywords:

Brin prize,
Sarig.

Mathematics Subject Classification: 37D40, 37D25, 37D40.

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