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dc.contributor.authorCioletti, Leandro Martins-
dc.contributor.authorMelo, Leonardo-
dc.contributor.authorRuviaro, Ricardo-
dc.contributor.authorSilva, Eduardo Antônio da-
dc.identifier.citationCIOLETTI, 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:
dc.rightsAcesso Restritopt_BR
dc.titleOn the dimension of the space of harmonic functions on transitive shift spacespt_BR
dc.subject.keywordMecânica estatísticapt_BR
dc.subject.keywordFunções harmônicaspt_BR
dc.subject.keywordPrincípio de invariânciapt_BR
dc.subject.keywordProcessos de Markovpt_BR
dc.description.abstract1In 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
Appears in Collections:MAT - Artigos publicados em periódicos e preprints

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