On the recurrence of random walks on Z in random medium

Abstract

We study random walks on $\text{Z}$ in a stationary random medium, defined by an ergodic dynamical system, when the possible jumps are {0,±1,±2}. We give a simple proof of a recurrence criterion of the same kind as Key's [6]. We show that the intermediate Lyapunov exponent involved in the criterion is always simple.