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Bulk diffusion in a system with site disorder

Jeremy Quastel
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Abstract

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.

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Jeremy Quastel. 2006-11-21. Bulk diffusion in a system with site disorder. https://doi.org/10.1214/009117906000000322

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