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Bulk diffusion of 1D exclusion process with bond disorder

A. Faggionato
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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.

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A. Faggionato. 2006-01-04. Bulk diffusion of 1D exclusion process with bond disorder. https://arxiv.org/abs/math/0601076

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