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Título : On the dimension of the space of harmonic functions on transitive shift spaces
Autor : Cioletti, Leandro Martins
Melo, Leonardo
Ruviaro, Ricardo
Silva, Elves Alves de Barros e
Assunto:: Mecânica estatística
Funções harmônicas
Princípio de invariância
Processos de Markov
Fecha de publicación : 21-abr-2021
Editorial : Elsevier
Citación : 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
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