Symmetric exclusion as a model of non-elliptic dynamical random conductances

2012/06/08 by L. Avena, Avena, L.
Mathematics · #60K37 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60K37

paper · pdf · doi:10.48550/arxiv.1206.1817

Preliminary version, any comments are welcome. 9 pages

arxiv created 2012/06/08 · arxiv updated 2012/06/11

Abstract

We consider a finite range symmetric exclusion process on the integer lattice in any dimension. We interpret it as a non-elliptic time-dependent random conductance model by setting conductances equal to one over the edges with end points occupied by particles of the exclusion process and to zero elsewhere. We prove a law of large number and a central limit theorem for the random walk driven by such a dynamical field of conductances by using the Kipnis-Varhadan martingale approximation. Unlike the tagged particle in the exclusion process, which is in some sense similar to this model, this random walk is diffusive even in the one-dimensional nearest-neighbor case.

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