Random walks in a random environment on a strip: a renormalization group approach

Abstract

We present a real space renormalization group scheme for the problem of random walks in a random environment on a strip, which includes the one-dimensional random walk in a random environment with bounded non-nearest-neighbour jumps. We show that the model renormalizes to an effective one-dimensional random walk with nearest-neighbour jumps and conclude that Sinai scaling is valid in the recurrent case, while in the sub-linear transient phase, the displacement grows as a power of the time.