2006/01/31 by Jeremy Quastel
Mathematics · Physics and Astronomy · #Markov Chains and Monte Carlo Methods #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR #msc:60K35 #msc:60K37 #msc:82C44
paper · pdf · doi:10.1214/009117906000000322
published as Annals of Probability 2006, Vol. 34, No. 5, 1990-2036 · 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)
openalex publication_date 2006/09/01 · arxiv created 2006/11/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.