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

We consider a one-dimensional simple symmetric exclusion process in equilibrium as a dynamic random environment for a nearest-neighbor random walk that on occupied/vacant sites has two different local drifts to the right. We obtain a LLN, a functional CLT and large deviation bounds for the random walk under the annealed measure by means of a renewal argument. We also obtain an Einstein relation under a suitable perturbation. A brief discussion on the topic of random walks in slowly mixing dynamic random environments is presented.