Recurrence and Transience Criteria for Random Walk in a Random Environment

Abstract

Oseledec's Multiplicative Ergodic Theorem is used to give recurrence and transience criteria for random walk in a random environment on the integers. These criteria generalize those given by Solomon in the nearest-neighbor case. The methodology for random environments is then applied to Markov chains with periodic transition functions to obtain recurrence and transience criteria for these processes as well.