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Title: On the dimension of the space of harmonic functions on transitive shift spaces
Authors: Cioletti, Leandro Martins
Melo, Leonardo
Ruviaro, Ricardo
Silva, Eduardo Antônio da
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:
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.
Appears in Collections:MAT - Artigos publicados em periódicos e preprints

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