| Full text | |
| Author(s): |
Armendariz, Ines
[1]
;
Ferrari, Pablo A.
[2, 1, 3]
;
Groisman, Pablo
[1, 3]
;
Leonardi, Florencia
[2]
Total Authors: 4
|
| Affiliation: | [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
Total Affiliations: 3
|
| Document type: | Journal article |
| Source: | Journal of Statistical Physics; v. 158, n. 6, p. 1213-1233, MAR 2015. |
| Web of Science Citations: | 0 |
| Abstract | |
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) | |
| FAPESP's process: | 13/07699-0 - Research, Innovation and Dissemination Center for Neuromathematics - NeuroMat |
| Grantee: | Oswaldo Baffa Filho |
| Support Opportunities: | Research Grants - Research, Innovation and Dissemination Centers - RIDC |