Bulk diffusion of 1D exclusion process with bond disorder

Abstract

Given a doubly infinite sequence of positive numbers {c_k: k in Z} satisfying a LLN with limit A, we consider the nearest-neighbor simple exclusion process on Z where c_k is the probability rate of jumps between k and k+1. If A is infinite we require an additional minor technical condition. By extending a method developed by K. Nagy, we show that the diffusively rescaled process has hydrodynamic behavior described by the heat equation with diffusion constant 1/A. In particular, the process has diffusive behavior for finite A and subdiffusive behavior for infinite A.

18 pages, extentions, final version (2007)

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• Stochastic homogenization in amorphous media and applications to exclusion processes
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• Euler hydrodynamics for attractive particle systems in random environment