{"title":"无穷图的有限子图对应的平衡测度的收敛性:新例子","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":"{\"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}","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}
Convergence of equilibrium measures corresponding to finite subgraphs of infinite graphs: New examples
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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