INVESTIGADORES
FERRARI pablo Augusto
artículos
Título:
Finite Cycle Gibbs Measures on Permutations of Zd
Autor/es:
ARMENDARIZ INES; PABLO A. FERRARI; PABLO GROISMAN; FLORENCIA LEONARDI
Revista:
JOURNAL OF STATISTICAL PHYSICS
Editorial:
SPRINGER
Referencias:
Lugar: Berlin; Año: 2015 p. 1213 - 1233
ISSN:
0022-4715
Resumen:
We consider Gibbs distributions on the set of permutations of Zd associated to the Hamiltonian H(σ):=∑xV(σ(x)−x), where σ is a permutation and V:Zd→R is a strictly convex potential. Call finite-cycle those permutations composed by finite cycles only. We give conditions on V ensuring that for large enough temperature α>0 there exists a unique infinite volume ergodic Gibbs measure μα concentrating mass on finite-cycle permutations; this measure is equal to the thermodynamic limit of the specifications with identity boundary conditions. We construct μα 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 Fern\'andez, Ferrari and Garcia. Define τv as the shift permutation τv(x)=x+v. In the Gaussian case V=∥⋅∥2, we show that for each v∈Zd, μαv given by μαv(f)=μα[f(τv⋅)] is an ergodic Gibbs measure equal to the thermodynamic limit of the specifications with τv boundary conditions. For a general potential V, we prove the existence of Gibbs measures μαv when α is bigger than some v-dependent value.