vix.ing · top · new · best · stats · spec

Equivalence of ensembles for two-species zero-range invariant measures

2006/08/31 by Stefan Grosskinsky, Stefan Großkinsky
Mathematics · Physics and Astronomy · #Entropy (arrow of time) #Equivalence (formal languages) #Invariant (physics) #Markov Chains and Monte Carlo Methods #Mathematical analysis #Mathematical physics #Mathematics #Phase transition #Physics #Pure mathematics #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech #math-ph #math.MP #math.PR #msc:60K35 #msc:82B26 #msc:82C22

paper · pdf · doi:10.1016/j.spa.2007.09.006

published as Stoch. Proc. Appl. 118(8), 1322-1350 (2008) · 37 pages, 4 figures. Appeared online in Stoch. Proc. Appl

openalex publication_date 2007/09/26 · arxiv created 2008/01/09 · arxiv updated 2018/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We study the equivalence of ensembles for stationary measures of interacting particle systems with two conserved quantities and unbounded local state space. The main motivation is a condensation transition in the zero-range process which has recently attracted attention. Establishing the equivalence of ensembles via convergence in specific relative entropy, we derive the phase diagram for the condensation transition, which can be understood in terms of the domain of grand-canonical measures. Of particular interest, also from a mathematical point of view, are the convergence properties of the Gibbs free energy on the boundary of that domain, involving large deviations and multivariate local limit theorems of subexponential distributions.

Citations