Hydrodynamic limit of symmetric exclusion processes in inhomogeneous media

2010/03/29 by Faggionato, A.
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.1003.5521

Abstract

In \citeJ M. Jara has presented a method, reducing the proof of the hydrodynamic limit of symmetric exclusion processes to an homogenization problem, as unified approach to recent works on the field as \citeN, \citeF1, \citeF2 and \citeFJL. Although not stated in \citeJ, the reduction of the hydrodynamic limit to an homogenization problem was already obtained (in a different way) in \citeN, \citeF1. This alternative and very simple relation between the two problems goes back to an idea of K. Nagy \citeN, is stated in \citeF1[Section B] for exclusion processes on \bbZ^d and, as stressed in \citeF2, is completely general. The above relation has been applied to \citeN, \citeF1, \citeF2 and \citeFJL and could be applied to other symmetric exclusion processes, mentioned in \citeJ. In this short note we briefly recall this unified approach in a complete general setting. Finally, we recall how the homogenization problem has been solved in the above previous works.

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