Bulk diffusion in a system with site disorder
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.
Cite
@article{arxiv.math/0601124,
title = {Bulk diffusion in a system with site disorder},
author = {Jeremy Quastel},
journal= {arXiv preprint arXiv:math/0601124},
year = {2007}
}
Comments
Published at http://dx.doi.org/10.1214/009117906000000322 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)