Finite Cycle Gibbs Measures on Permutations of Zd

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 condi...

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Autores principales: Armendáriz, I., Ferrari, P.A., Groisman, P., Leonardi, F.
Formato: JOUR
Materias:
Cycles
Ergodicity
Gibbs measures
Hamiltonian
Invariant measure
Permutations
Specifications
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00224715_v158_n6_p1213_Armendariz
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_00224715_v158_n6_p1213_Armendariz2023-10-03T14:32:57Z Finite Cycle Gibbs Measures on Permutations of Zd Armendáriz, I. Ferrari, P.A. Groisman, P. Leonardi, F. Cycles Ergodicity Gibbs measures Hamiltonian Invariant measure Permutations Specifications 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00224715_v158_n6_p1213_Armendariz
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Cycles
Ergodicity
Gibbs measures
Hamiltonian
Invariant measure
Permutations
Specifications
spellingShingle Cycles
Ergodicity
Gibbs measures
Hamiltonian
Invariant measure
Permutations
Specifications
Armendáriz, I.
Ferrari, P.A.
Groisman, P.
Leonardi, F.
Finite Cycle Gibbs Measures on Permutations of Zd
topic_facet Cycles
Ergodicity
Gibbs measures
Hamiltonian
Invariant measure
Permutations
Specifications
description 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.
format JOUR
author Armendáriz, I.
Ferrari, P.A.
Groisman, P.
Leonardi, F.
author_facet Armendáriz, I.
Ferrari, P.A.
Groisman, P.
Leonardi, F.
author_sort Armendáriz, I.
title Finite Cycle Gibbs Measures on Permutations of Zd
title_short Finite Cycle Gibbs Measures on Permutations of Zd
title_full Finite Cycle Gibbs Measures on Permutations of Zd
title_fullStr Finite Cycle Gibbs Measures on Permutations of Zd
title_full_unstemmed Finite Cycle Gibbs Measures on Permutations of Zd
title_sort finite cycle gibbs measures on permutations of zd
url http://hdl.handle.net/20.500.12110/paper_00224715_v158_n6_p1213_Armendariz
work_keys_str_mv AT armendarizi finitecyclegibbsmeasuresonpermutationsofzd
AT ferraripa finitecyclegibbsmeasuresonpermutationsofzd
AT groismanp finitecyclegibbsmeasuresonpermutationsofzd
AT leonardif finitecyclegibbsmeasuresonpermutationsofzd
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