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.

Proceedings of II Escola Brasileira de Probabilidade (Barra do Sahy, Sao Paulo, August 1998)