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Bulk diffusion in a system with site disorder. (English) Zbl 1104.60066

Summary: We consider a system of random walks in a random environment interacting via exclusion. The model is reversible with respect to a family of disordered Bernoulli measures. Assuming some weak mixing conditions, it is shown that, under diffusive scaling, the system has a deterministic hydrodynamic limit which holds for almost every realization of the environment. The limit is a nonlinear diffusion equation with diffusion coefficient given by a variational formula. The model is nongradient and the method used is the “long jump” variation of the standard nongradient method, which is a type of renormalization. The proof is valid in all dimensions.

MSC:

60K37 Processes in random environments
60K35 Interacting random processes; statistical mechanics type models; percolation theory
82C44 Dynamics of disordered systems (random Ising systems, etc.) in time-dependent statistical mechanics
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References:

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