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 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 recurren...

Abstract We study a random walk in a random environment (RWRE) on Z, 1 ≤ d < +∞. The main assumption is that conditionned on the environment the random walk is reversible. Moreover we construct our environment in such a way the walk can’t be trapped on a single point like in some particular RWRE but in some specific d-1 surfaces. These surfaces are basic surfaces with deterministic geometry. We...