{"title":"Convergence of equilibrium measures corresponding to finite subgraphs of infinite graphs: New examples","authors":"B. Gurevich","doi":"10.1090/conm/772/15487","DOIUrl":null,"url":null,"abstract":"A problem from thermodynamic formalism for countable symbolic Markov chains is considered. It concerns asymptotic behavior of the equilibrium measures corresponding to increasing sequences of finite submatrices of an infinite nonnegative matrix \n\n \n A\n A\n \n\n when these sequences converge to \n\n \n A\n A\n \n\n. After reviewing the results obtained up to now, a solution of the problem is given for a new matrix class. The geometric language of loaded graphs is used, instead of the matrix language.","PeriodicalId":296603,"journal":{"name":"Topology, Geometry, and Dynamics","volume":"72 6 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Topology, Geometry, and Dynamics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/conm/772/15487","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
A problem from thermodynamic formalism for countable symbolic Markov chains is considered. It concerns asymptotic behavior of the equilibrium measures corresponding to increasing sequences of finite submatrices of an infinite nonnegative matrix
A
A
when these sequences converge to
A
A
. After reviewing the results obtained up to now, a solution of the problem is given for a new matrix class. The geometric language of loaded graphs is used, instead of the matrix language.
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