Bulk diffusion of 1D exclusion process with bond disorder
Abstract
Given a doubly infinite sequence of positive numbers ck: k in Z satisfying a LLN with limit A, we consider the nearest-neighbor simple exclusion process on Z where ck 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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