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.
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Received: 11 November 1996/In revised form: 10 October 1997
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Bahadoran, C. Hydrodynamical limit for spatially heterogeneous simple exclusion processes. Probab Theory Relat Fields 110, 287–331 (1998). https://doi.org/10.1007/s004400050150
- Mathematics Subject Classification (1991): 60K35