Bulk diffusion of 1D exclusion process with bond disorder
Probability
2010-03-31 v3 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.math/0601076,
title = {Bulk diffusion of 1D exclusion process with bond disorder},
author = {A. Faggionato},
journal= {arXiv preprint arXiv:math/0601076},
year = {2010}
}
Comments
18 pages, extentions, final version (2007)