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Armendáriz, I.; Ferrari, P.A.; Groisman, P.; Leonardi, F. "Finite Cycle Gibbs Measures on Permutations of Zd" (2015) Journal of Statistical Physics. 158(6):1213-1233
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Abstract:

We consider Gibbs distributions on the set of permutations of Zd associated to the Hamiltonian (Formula Presented.), where (Formula Presented.) is a permutation and (Formula Presented.) is a strictly convex potential. Call finite-cycle those permutations composed by finite cycles only. We give conditions on (Formula Presented.) ensuring that for large enough temperature (Formula Presented.) there exists a unique infinite volume ergodic Gibbs measure (Formula Presented.) concentrating mass on finite-cycle permutations; this measure is equal to the thermodynamic limit of the specifications with identity boundary conditions. We construct (Formula Presented.) 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 Fernández, Ferrari and Garcia. Define (Formula Presented.) as the shift permutation (Formula Presented.). In the Gaussian case (Formula Presented.), we show that for each (Formula Presented.), (Formula Presented.) given by (Formula Presented.) is an ergodic Gibbs measure equal to the thermodynamic limit of the specifications with (Formula Presented.) boundary conditions. For a general potential (Formula Presented.), we prove the existence of Gibbs measures (Formula Presented.) when (Formula Presented.) is bigger than some v-dependent value. © 2014, Springer Science+Business Media New York.

Registro:

Documento: Artículo
Título:Finite Cycle Gibbs Measures on Permutations of Zd
Autor:Armendáriz, I.; Ferrari, P.A.; Groisman, P.; Leonardi, F.
Filiación:Departamento de Matemática, Universidad de Buenos Aires, Buenos Aires, Argentina
Departamento de Matemática, Universidad de Buenos Aires and IMAS-CONICET, Buenos Aires, Argentina
Instituto de Matemática e Estatística, Universidade de São Paulo, São Paulo, Brazil
Palabras clave:Cycles; Ergodicity; Gibbs measures; Hamiltonian; Invariant measure; Permutations; Specifications
Año:2015
Volumen:158
Número:6
Página de inicio:1213
Página de fin:1233
DOI: http://dx.doi.org/10.1007/s10955-014-1169-6
Título revista:Journal of Statistical Physics
Título revista abreviado:J. Stat. Phys.
ISSN:00224715
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00224715_v158_n6_p1213_Armendariz

Referencias:

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Citas:

---------- APA ----------
Armendáriz, I., Ferrari, P.A., Groisman, P. & Leonardi, F. (2015) . Finite Cycle Gibbs Measures on Permutations of Zd. Journal of Statistical Physics, 158(6), 1213-1233.
http://dx.doi.org/10.1007/s10955-014-1169-6
---------- CHICAGO ----------
Armendáriz, I., Ferrari, P.A., Groisman, P., Leonardi, F. "Finite Cycle Gibbs Measures on Permutations of Zd" . Journal of Statistical Physics 158, no. 6 (2015) : 1213-1233.
http://dx.doi.org/10.1007/s10955-014-1169-6
---------- MLA ----------
Armendáriz, I., Ferrari, P.A., Groisman, P., Leonardi, F. "Finite Cycle Gibbs Measures on Permutations of Zd" . Journal of Statistical Physics, vol. 158, no. 6, 2015, pp. 1213-1233.
http://dx.doi.org/10.1007/s10955-014-1169-6
---------- VANCOUVER ----------
Armendáriz, I., Ferrari, P.A., Groisman, P., Leonardi, F. Finite Cycle Gibbs Measures on Permutations of Zd. J. Stat. Phys. 2015;158(6):1213-1233.
http://dx.doi.org/10.1007/s10955-014-1169-6