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

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  • Großkinsky, Stefan

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.

Suggested Citation

  • Großkinsky, Stefan, 2008. "Equivalence of ensembles for two-species zero-range invariant measures," Stochastic Processes and their Applications, Elsevier, vol. 118(8), pages 1322-1350, August.
    • Handle: RePEc:eee:spapps:v:118:y:2008:i:8:p:1322-1350
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    References listed on IDEAS

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    1. Touchette, Hugo & Ellis, Richard S. & Turkington, Bruce, 2004. "An introduction to the thermodynamic and macrostate levels of nonequivalent ensembles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 340(1), pages 138-146.
    2. Benjamini, I. & Ferrari, P. A. & Landim, C., 1996. "Asymmetric conservative processes with random rates," Stochastic Processes and their Applications, Elsevier, vol. 61(2), pages 181-204, February.
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    Cited by:

    1. Armendáriz, Inés & Grosskinsky, Stefan & Loulakis, Michail, 2013. "Zero-range condensation at criticality," Stochastic Processes and their Applications, Elsevier, vol. 123(9), pages 3466-3496.

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