Bulk diffusion in a system with site disorder

Details Bulk diffusion in a system with site disorder Bulk diffusion in a system with site disorder

2006-01-06

arxiv.org/abs/math/0601124v2

Annals of Probability 2006, Vol. 34, No. 5, 1990-2036

Mathematics

Probability

Published at http://dx.doi.org/10.1214/009117906000000322 in the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

10.1214/009117906000000322

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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