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We consider a one-dimensional simple symmetric exclusion process inequilibrium, constituting a dynamic random environment for a nearest-neighborrandom walk that on occupied/vacant sites has two different local drifts to theright. We construct a renewal structure from which a LLN, a functional CLT andlarge deviation bounds for the random walk under the annealed measure follow.We further prove an Einstein relation under a suitable perturbation. A briefdiscussion on the topic of random walks in slowly mixing dynamic randomenvironments is presented.

Transient random walk in symmetric exclusion: limit theorems and an Einstein relation