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Finite Cycle Gibbs Measures on Permutations of Z(d)

Texto completo
Autor(es):
Armendariz, Ines [1] ; Ferrari, Pablo A. [2, 1, 3] ; Groisman, Pablo [1, 3] ; Leonardi, Florencia [2]
Número total de Autores: 4
Afiliação do(s) autor(es):
[1] Univ Buenos Aires, Dept Matemat, Buenos Aires, DF - Argentina
[2] Univ Sao Paulo, Inst Matemat & Estatist, Sao Paulo - Brazil
[3] IMAS CONICET, Buenos Aires, DF - Argentina
Número total de Afiliações: 3
Tipo de documento: Artigo Científico
Fonte: Journal of Statistical Physics; v. 158, n. 6, p. 1213-1233, MAR 2015.
Citações Web of Science: 0
Resumo

We consider Gibbs distributions on the set of permutations of associated to the Hamiltonian , where is a permutation and is a strictly convex potential. Call finite-cycle those permutations composed by finite cycles only. We give conditions on ensuring that for large enough temperature there exists a unique infinite volume ergodic Gibbs measure concentrating mass on finite-cycle permutations; this measure is equal to the thermodynamic limit of the specifications with identity boundary conditions. We construct as the unique invariant measure of a Markov process on the set of finite-cycle permutations that can be seen as a loss-network, a continuous-time birth and death process of cycles interacting by exclusion, an approach proposed by Fernandez, Ferrari and Garcia. Define as the shift permutation . In the Gaussian case , we show that for each , given by is an ergodic Gibbs measure equal to the thermodynamic limit of the specifications with boundary conditions. For a general potential , we prove the existence of Gibbs measures when is bigger than some -dependent value. (AU)

Processo FAPESP: 13/07699-0 - Centro de Pesquisa, Inovação e Difusão em Neuromatemática - NeuroMat
Beneficiário:Jefferson Antonio Galves
Linha de fomento: Auxílio à Pesquisa - Centros de Pesquisa, Inovação e Difusão - CEPIDs