Supercritical behavior of asymmetric zero-range process with sitewise disorder

TL;DR

This paper characterizes the conditions under which asymmetric zero-range processes with sitewise disorder converge to an invariant measure, broadening previous models and simplifying existing proofs.

Contribution

It provides necessary and sufficient conditions for convergence in a broader class of asymmetric zero-range processes with sitewise disorder, along with a simplified proof of a known result.

Findings

Established convergence conditions for asymmetric zero-range processes

Broadened the class of environments considered

Provided a simpler proof of existing results

Abstract

We establish necessary and sufficient conditions for weak convergence to the upper invariant measure for asymmetric nearest neighbour zero range processes with non homogeneous jump rates. The class of environments considered is close to that considered by Andjel, Ferrari, Guiol and Landim, while our class of processes is broader. We also give a simpler proof of a result of Ferrari and Sisko with weaker assumptions.