Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Hydrodynamical limit for spatially heterogeneous simple exclusion processes

  • 71 Accesses

  • 7 Citations


We prove hydrodynamical limit for spatially heterogeneous, asymmetric simple exclusion processes on Z d. The jump rate of particles depends on the macroscopic position x through some nonnegative, smooth velocity profile α(x). Hydrodynamics are described by the entropy solution to a spatially heterogeneous conservation law of the form

To derive this result, we prove an alternative characterization of entropy solutions involving stationary solutions, and work with macroscopically stationary states rather than the unknown stationary measures of the process. The method can be extended to spatially heterogeneous, asymmetric misanthrope processes with slow birth and death.

This is a preview of subscription content, log in to check access.

Author information

Additional information

Received: 11 November 1996/In revised form: 10 October 1997

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Bahadoran, C. Hydrodynamical limit for spatially heterogeneous simple exclusion processes. Probab Theory Relat Fields 110, 287–331 (1998). https://doi.org/10.1007/s004400050150

Download citation

  • Mathematics Subject Classification (1991): 60K35
  • 82C22