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Recent results and open problems on the hydrodynamics of disordered asymmetric exclusion and zero-range processes. (English) Zbl 1035.60093

Summary: 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 \(\mathbb{Z}^d\). 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. But to fully understand the phase transition, results on a finer scale are needed.

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
82C22 Interacting particle systems in time-dependent statistical mechanics
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