Quenched convergence and strong local equilibrium for asymmetric zero-range process with site disorder

TL;DR

This paper investigates the behavior of asymmetric zero-range processes with site disorder, establishing conditions for local equilibrium and mass loss across different density regimes without relying on initial local Gibbs states.

Contribution

It proves quenched strong local equilibrium and mass loss at supercritical densities for asymmetric zero-range processes with site disorder, relaxing previous assumptions.

Findings

Proves quenched strong local equilibrium at subcritical and critical densities.

Establishes dynamic local loss of mass at supercritical densities.

Shows convergence from initial configurations with asymptotic particle density.

Abstract

We study asymmetric zero-range processes on Z with nearest-neighbour jumps and site disorder. The jump rate of particles is an arbitrary but bounded nondecreasing function of the number of particles. We prove quenched strong local equilibrium at subcritical and critical hydrodynamic densities, and dynamic local loss of mass at supercritical hydrodynamic densities. Our results do not assume starting from local Gibbs states. As byproducts of these results, we prove convergence of the process from given initial configurations with an asymptotic density of particles to the left of the origin. In particular , we relax the weak convexity assumption of [7, 8] for the escape of mass property. 1 MSC 2010 subject classification: 60K35, 82C22.