Condensation in stochastic particle systems with stationary product measures

TL;DR

This paper analyzes condensation phenomena in stochastic particle systems with stationary product measures, providing a comprehensive characterization of the transition and establishing ensemble equivalence in both homogeneous and inhomogeneous settings.

Contribution

It offers a general framework for understanding condensation transitions and proves ensemble equivalence under broad conditions using entropy and local limit theorems.

Findings

Strengthened convergence results for subcritical systems

Established ensemble equivalence for inhomogeneous systems

Extended previous results to more general conditions

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.