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

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...

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Bibliographic Details
Published in:Stochastic processes and their applications 2008-08, Vol.118 (8), p.1322-1350
Main Author: GROSSKINSKY, Stefan
Format: Article
Language:English
Subjects:
Condensation transition
Equivalence of ensembles
Exact sciences and technology
Limit theorems
Mathematics
Probability and statistics
Probability theory and stochastic processes
Probability theory on algebraic and topological structures
Relative entropy
Sciences and techniques of general use
Stochastic analysis
Stochastic processes
Zero-range process
Zero-range process Equivalence of ensembles Condensation transition Relative entropy
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Summary: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.
ISSN:0304-4149
1879-209X
DOI:10.1016/j.spa.2007.09.006