Recent results and open problems on the hydrodynamics of disordered asymmetric exclusion and zero-range processes

Abstract

This paper summarizes results and some open problems about the large-scale and long-time behavior of asymmetric, disordered exclusion and zero-range processes. These processes have randomly chosen jump rates at the sites of the underlying lattice. The interesting feature is that for suitably distributed random rates there is a phase transition where the process behaves differently at high and low densities. Some of this distinction is visible on the hydrodynamic scale.