Hydrodynamic limit of simple exclusion processes in symmetric random environments via duality and homogenization

Abstract We consider continuous-time random walks on a locally finite subset of $$\mathbb {R}^d$$ R d with symmetric jump probability rates. The range can be unbounded. assume some second-moment conditions and that the above randomness is left invariant by action group {G}=\mathbb G = or {Z}^d$$ Z . then add site-exclusion interaction, thus making particle system simple exclusion process. show that, for almost all environments, under diffusive space–time rescaling exhibits hydrodynamic limit in path space. equation non-random governed effective homogenized matrix D single walk, which degenerate. result covers very large family models including e.g. processes built from conductance crystal lattices (possibly long conductances), Mott variable hopping, Delaunay triangulations, supercritical percolation clusters.