The Annals of Probability

Bulk diffusion in a system with site disorder

Jeremy Quastel

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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.

Article information

Source
Ann. Probab., Volume 34, Number 5 (2006), 1990-2036.

Dates
First available in Project Euclid: 14 November 2006

Permanent link to this document
https://projecteuclid.org/euclid.aop/1163517231

Digital Object Identifier
doi:10.1214/009117906000000322

Mathematical Reviews number (MathSciNet)
MR2271489

Zentralblatt MATH identifier
1104.60066

Subjects
Primary: 60K37: Processes in random environments 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82C44: Dynamics of disordered systems (random Ising systems, etc.)

Keywords
Hydrodynamic limit disordered systems

Citation

Quastel, Jeremy. Bulk diffusion in a system with site disorder. Ann. Probab. 34 (2006), no. 5, 1990--2036. doi:10.1214/009117906000000322. https://projecteuclid.org/euclid.aop/1163517231


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