On the dimension of the space of harmonic functions on transitive shift spaces

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MetadadosDescriçãoIdioma
Autor(es): dc.creatorCioletti, Leandro Martins-
Autor(es): dc.creatorMelo, Leonardo-
Autor(es): dc.creatorRuviaro, Ricardo-
Autor(es): dc.creatorSilva, Eduardo Antônio da-
Data de aceite: dc.date.accessioned2021-10-14T17:36:38Z-
Data de disponibilização: dc.date.available2021-10-14T17:36:38Z-
Data de envio: dc.date.issued2021-06-18-
Data de envio: dc.date.issued2021-06-18-
Data de envio: dc.date.issued2021-04-21-
Fonte completa do material: dc.identifierhttps://repositorio.unb.br/handle/10482/41196-
Fonte completa do material: dc.identifierhttps://doi.org/10.1016/j.aim.2021.107758-
Fonte: dc.identifier.urihttp://educapes.capes.gov.br/handle/capes/611982-
Descrição: dc.descriptionIn this paper, we show a new relation between phase transition in Statistical Mechanics and the dimension of the space of harmonic functions (SHF) for a transfer operator. This is accomplished by extending the classical Ruelle-Perron-Frobenius theory to the realm of low regular potentials defined on either finite or infinite (uncountable) alphabets. We also give an example of a potential having a phase transition where the Perron-Frobenius eigenvector space has dimension two. We discuss entropy and equilibrium states, in this general setting, and show that if the SHF is non-trivial, then the associated equilibrium states have full support. We also obtain a weak invariance principle in cases where the spectral gap property is absent. As a consequence, a functional central limit theorem for non-local observables of the Dyson model is obtained.-
Publicador: dc.publisherElsevier-
Relação: dc.relationhttps://www.sciencedirect.com/science/article/abs/pii/S0001870821001973-
Direitos: dc.rightsAcesso Restrito-
Palavras-chave: dc.subjectMecânica estatística-
Palavras-chave: dc.subjectFunções harmônicas-
Palavras-chave: dc.subjectPrincípio de invariância-
Palavras-chave: dc.subjectProcessos de Markov-
Título: dc.titleOn the dimension of the space of harmonic functions on transitive shift spaces-
Tipo de arquivo: dc.typelivro digital-
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