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

Cioletti, Leandro Martins; Melo, Leonardo; Ruviaro, Ricardo; Silva, Elves Alves de Barros e

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dc.contributor.author	Cioletti, Leandro Martins	-
dc.contributor.author	Melo, Leonardo	-
dc.contributor.author	Ruviaro, Ricardo	-
dc.contributor.author	Silva, Elves Alves de Barros e	-
dc.date.accessioned	2021-06-18T12:42:09Z	-
dc.date.available	2021-06-18T12:42:09Z	-
dc.date.issued	2021-04-21	-
dc.identifier.citation	CIOLETTI, L. et al. On the dimension of the space of harmonic functions on transitive shift spaces. Advances in Mathematics, v. 385, 107758, 16 jul. 2021. DOI: https://doi.org/10.1016/j.aim.2021.107758.	pt_BR
dc.identifier.uri	https://repositorio.unb.br/handle/10482/41196	-
dc.language.iso	Inglês	pt_BR
dc.publisher	Elsevier	pt_BR
dc.rights	Acesso Restrito	pt_BR
dc.title	On the dimension of the space of harmonic functions on transitive shift spaces	pt_BR
dc.type	Artigo	pt_BR
dc.subject.keyword	Mecânica estatística	pt_BR
dc.subject.keyword	Funções harmônicas	pt_BR
dc.subject.keyword	Princípio de invariância	pt_BR
dc.subject.keyword	Processos de Markov	pt_BR
dc.identifier.doi	https://doi.org/10.1016/j.aim.2021.107758	pt_BR
dc.relation.publisherversion	https://www.sciencedirect.com/science/article/abs/pii/S0001870821001973	pt_BR
dc.description.abstract1	In 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.	pt_BR
dc.description.unidade	Instituto de Ciências Exatas (IE)	-
dc.description.unidade	Departamento de Matemática (IE MAT)	-
Collection(s) :	Artigos publicados em periódicos e afins