Thermodynamic Formalism For Amenable Groups and Countable State Spaces.

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Given the full shift over a countable state space on a countable amenable group, we develop its thermodynamic formalism. First, we introduce the concept of pressure and, using tiling techniques, prove its existence and further properties, such as an infimum rule. Next, we extend the definitions of d...

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Detalles Bibliográficos
Autores: Beltrán, Elmer R, Borsato, Luísa, Bissacot, Rodrigo, Briceño, Raimundo
Formato: artículo
Fecha de Publicación:2024
Institución:Universidad Nacional de Moquegua
Repositorio:UNAM-Institucional
Lenguaje:inglés
OAI Identifier:oai:repositorio.unam.edu.pe:UNAM/598
Enlace del recurso:https://repositorio.unam.edu.pe/handle/UNAM/598
https://doi.org/10.1017/S1474748024000112
Nivel de acceso:acceso abierto
Materia:Amenable group.
Countable state space
Gibbs measure.
Pressure.
Thermodynamic formalism.
https://purl.org/pe-repo/ocde/ford#1.01.00
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dc.title.none.fl_str_mv Thermodynamic Formalism For Amenable Groups and Countable State Spaces.
title Thermodynamic Formalism For Amenable Groups and Countable State Spaces.
spellingShingle Thermodynamic Formalism For Amenable Groups and Countable State Spaces.
Beltrán, Elmer R
Amenable group.
Countable state space
Gibbs measure.
Pressure.
Thermodynamic formalism.
https://purl.org/pe-repo/ocde/ford#1.01.00
title_short Thermodynamic Formalism For Amenable Groups and Countable State Spaces.
title_full Thermodynamic Formalism For Amenable Groups and Countable State Spaces.
title_fullStr Thermodynamic Formalism For Amenable Groups and Countable State Spaces.
title_full_unstemmed Thermodynamic Formalism For Amenable Groups and Countable State Spaces.
title_sort Thermodynamic Formalism For Amenable Groups and Countable State Spaces.
author Beltrán, Elmer R
author_facet Beltrán, Elmer R
Borsato, Luísa
Bissacot, Rodrigo
Briceño, Raimundo
author_role author
author2 Borsato, Luísa
Bissacot, Rodrigo
Briceño, Raimundo
author2_role author
author
author
dc.contributor.author.fl_str_mv Beltrán, Elmer R
Borsato, Luísa
Bissacot, Rodrigo
Briceño, Raimundo
dc.subject.en.fl_str_mv Amenable group.
Countable state space
Gibbs measure.
Pressure.
Thermodynamic formalism.
topic Amenable group.
Countable state space
Gibbs measure.
Pressure.
Thermodynamic formalism.
https://purl.org/pe-repo/ocde/ford#1.01.00
dc.subject.ocde.none.fl_str_mv https://purl.org/pe-repo/ocde/ford#1.01.00
description Given the full shift over a countable state space on a countable amenable group, we develop its thermodynamic formalism. First, we introduce the concept of pressure and, using tiling techniques, prove its existence and further properties, such as an infimum rule. Next, we extend the definitions of different notions of Gibbs measures and prove their existence and equivalence, given some regularity and normalization criteria on the potential. Finally, we provide a family of potentials that nontrivially satisfy the conditions for having this equivalence and a nonempty range of inverse temperatures where uniqueness holds. © The Author(s), 2024.
publishDate 2024
dc.date.accessioned.none.fl_str_mv 2024-10-04T16:50:17Z
dc.date.available.none.fl_str_mv 2024-10-04T16:50:17Z
dc.date.issued.fl_str_mv 2024-03-15
dc.type.none.fl_str_mv info:eu-repo/semantics/article
dc.type.version.none.fl_str_mv info:eu-repo/semantics/publishedVersion
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dc.identifier.uri.none.fl_str_mv https://repositorio.unam.edu.pe/handle/UNAM/598
dc.identifier.doi.none.fl_str_mv https://doi.org/10.1017/S1474748024000112
url https://repositorio.unam.edu.pe/handle/UNAM/598
https://doi.org/10.1017/S1474748024000112
dc.language.iso.none.fl_str_mv eng
language eng
dc.relation.ispartof.none.fl_str_mv Journal of the Institute of Mathematics of Jussieu
dc.relation.uri.none.fl_str_mv https://doi.org/10.1017/S1474748024000112
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eu_rights_str_mv openAccess
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dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Cambridge University Press
publisher.none.fl_str_mv Cambridge University Press
dc.source.none.fl_str_mv Repositorio Institucional - UNAM
reponame:UNAM-Institucional
instname:Universidad Nacional de Moquegua
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spelling Beltrán, Elmer RBorsato, LuísaBissacot, RodrigoBriceño, Raimundo2024-10-04T16:50:17Z2024-10-04T16:50:17Z2024-03-15https://repositorio.unam.edu.pe/handle/UNAM/598https://doi.org/10.1017/S1474748024000112Given the full shift over a countable state space on a countable amenable group, we develop its thermodynamic formalism. First, we introduce the concept of pressure and, using tiling techniques, prove its existence and further properties, such as an infimum rule. Next, we extend the definitions of different notions of Gibbs measures and prove their existence and equivalence, given some regularity and normalization criteria on the potential. Finally, we provide a family of potentials that nontrivially satisfy the conditions for having this equivalence and a nonempty range of inverse temperatures where uniqueness holds. © The Author(s), 2024.application/pdfengCambridge University PressJournal of the Institute of Mathematics of Jussieuhttps://doi.org/10.1017/S1474748024000112info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/4.0Repositorio Institucional - UNAMreponame:UNAM-Institucionalinstname:Universidad Nacional de Moqueguainstacron:UNAMAmenable group.Countable state spaceGibbs measure.Pressure.Thermodynamic formalism.https://purl.org/pe-repo/ocde/ford#1.01.00Thermodynamic Formalism For Amenable Groups and Countable State Spaces.info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionLICENSElicense.txtlicense.txtapplication/octet_stream1748https://repositorio.unam.edu.pe/bitstreams/735e2a13-d921-4cfa-b42f-e5439a6ae2cf/download8a4605be74aa9ea9d79846c1fba20a33MD51ORIGINALTHUMBNAIL11.jpgapplication/octet_stream6123https://repositorio.unam.edu.pe/bitstreams/5c7d3027-cffc-48b7-8c22-33912ecb1807/download562ae53ce6ca99b2ec2e6825463265b4MD53UNAM/598oai:repositorio.unam.edu.pe:UNAM/5982024-10-04 11:54:39.885https://creativecommons.org/licenses/by/4.0info:eu-repo/semantics/openAccessmetadata.onlyhttps://repositorio.unam.edu.peRepositorio - Universidad Nacional de Moqueguadspace-help@myu.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Thermodynamic Formalism For Amenable Groups and Countable State Spaces.
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