Rate of relaxation for a mean-field zero-range process

TL;DR

This paper investigates the relaxation dynamics of a mean-field zero-range process on the complete graph, demonstrating rapid convergence to equilibrium via a fluid limit that approaches the Gibbs distribution.

Contribution

It provides a rigorous proof of the process's convergence to a fluid limit and characterizes the relaxation to the Gibbs distribution.

Findings

The zero-range process converges to a fluid limit.

The fluid limit rapidly relaxes to the Gibbs distribution.

The process exhibits mean-field behavior on the complete graph.

Abstract

We study the zero-range process on the complete graph. It is a Markov chain model for a microcanonical ensemble. We prove that the process converges to a fluid limit. The fluid limit rapidly relaxes to the appropriate Gibbs distribution.