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


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.


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Jeremy Quastel. "Bulk diffusion in a system with site disorder." Ann. Probab. 34 (5) 1990 - 2036, September 2006.


Published: September 2006
First available in Project Euclid: 14 November 2006

zbMATH: 1104.60066
MathSciNet: MR2271489
Digital Object Identifier: 10.1214/009117906000000322

Primary: 60K35 , 60K37 , 82C44

Keywords: Disordered systems , Hydrodynamic limit

Rights: Copyright © 2006 Institute of Mathematical Statistics

Vol.34 • No. 5 • September 2006
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