RANDOM-WALKS IN ASYMMETRIC RANDOM-ENVIRONMENTS

We consider random walks on Z(d) with transitions rates p(x, y) given by a random matrix. If p is a small random perturbation of the simple random walk, we show that the walk remains diffusive for almost all environments p if d > 2. The result also holds for a continuous time Markov process with a random drift. The corresponding path space measures converge weakly, in the scaling limit, to the Wiener process, for almost every p.