Bulk diffusion in a system with site disorder

• 成果类型: Article
• 署名作者: Quastel, Jeremy
• 署名单位: University of Toronto
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117906000000322
• 发表日期: 2006
• 页码: 1990-2036
• 关键词: hopping conductivity; hydrodynamic limit

摘要

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.