Supercriticality conditions for asymmetric zero-range process with sitewise disorder

TL;DR

This paper establishes the precise conditions under which a disordered asymmetric zero-range process converges to its critical invariant measures, enhancing understanding of phase transitions in disordered particle systems.

Contribution

It provides necessary and sufficient conditions for convergence to critical invariant measures in disordered asymmetric zero-range processes, a novel theoretical result.

Findings

Derived explicit convergence conditions

Identified critical invariant measures for disordered systems

Enhanced understanding of phase transition behavior

Abstract

We discuss necessary and sufficient conditions for the convergence of disordered asymmetric zero-range process to the critical invariant measures.