Computable criteria for ballisticity of random walks in elliptic random environment

Abstract

We consider random walks in i.i.d. elliptic random environments which are not uniformly elliptic. We introduce a computable condition in dimension d = 2 and a general condition valid for dimensions d ≥ 2 expressed in terms of the exit time from a box, which ensure that local trapping would not inhibit a ballistic behavior of the random walk. Furthermore, we prove that this general condition is sharp.