Title:	On the dimension of the space of harmonic functions on transitive shift spaces
Authors:	Cioletti, Leandro Martins Melo, Leonardo Ruviaro, Ricardo Silva, Elves Alves de Barros e
Assunto::	Mecânica estatística Funções harmônicas Princípio de invariância Processos de Markov
Issue Date:	21-Apr-2021
Publisher:	Elsevier
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.
Abstract:	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.
metadata.dc.description.unidade:	Instituto de Ciências Exatas (IE) Departamento de Matemática (IE MAT)
DOI:	https://doi.org/10.1016/j.aim.2021.107758
metadata.dc.relation.publisherversion:	https://www.sciencedirect.com/science/article/abs/pii/S0001870821001973
Appears in Collections:	Artigos publicados em periódicos e afins

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