Hydrodynamics in a condensation regime: The disordered asymmetric zero-range process

Abstract

We study asymmetric zero-range processes on $\mathbb{Z}$ with nearest-neighbour jumps and site disorder. The jump rate of particles is an arbitrary but bounded nondecreasing function of the number of particles. For any given environment satisfying suitable averaging properties, we establish a hydrodynamic limit given by a scalar conservation law including the domain above critical density, where the flux is shown to be constant.