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.
Jeremy Quastel. "Bulk diffusion in a system with site disorder." Ann. Probab. 34 (5) 1990 - 2036, September 2006. https://doi.org/10.1214/009117906000000322