Condensation in stochastic particle systems with stationary product measures

Abstract

We study stochastic particle systems with stationary product measures that exhibit a condensation transition due to particle interactions or spatial inhomogeneities. We review previous work on the stationary behaviour and put it in the context of the equivalence of ensembles, providing a general characterization of the condensation transition for homogeneous and inhomogeneous systems in the thermodynamic limit. This leads to strengthened results on weak convergence for subcritical systems, and establishes the equivalence of ensembles for spatially inhomogeneous systems under very general conditions, extending previous results which were focused on attractive and finite systems. We use relative entropy techniques which provide simple proofs, making use of general versions of local limit theorems for independent random variables.

44 pages, 4 figures; improved figures and corrected typographical errors

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Cited by in corpus (31)

• Equivalence and nonequivalence of ensembles: Thermodynamic, macrostate, and measure levels
• Anomalous scaling of dynamical large deviations
• Dynamics of condensation in the totally asymmetric inclusion process
• Condensation and Metastable Behavior of Non-reversible Inclusion Processes
• Coarsening dynamics in condensing zero-range processes and size-biased birth death chains
• Random partitions in statistical mechanics
• Hydrodynamic Limit of mean zero condensing Zero Range Processes with sub-critical initial profiles
• Structure of the condensed phase in the inclusion process
• Current large deviations for partially asymmetric particle systems on a ring
• Derivation of mean-field equations for stochastic particle systems
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• A dynamical transition and metastability in a size-dependent zero-range process
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• A mass transport model with a simple non-factorized steady-state distribution
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• Equivalence of ensembles, condensation and glassy dynamics in the Bose-Hubbard Hamiltonian
• On Random Allocation Models in the Thermodynamic Limit
• Size-biased diffusion limits and the inclusion process
• Condensation in models with factorized and pair-factorized stationary states
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• Estimation of local microcanonical averages in two lattice mean-field models using coupling techniques
• The role of zero-clusters in exchange-driven growth with and without input
• Generalized Young measures and the hydrodynamic limit of condensing zero range processes
• Partition function zeros of zeta-urns
• An algebraic approach to product-form stationary distributions for some reaction networks
• Yang-Lee zeros for real-space condensation
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