Random entropy and recurrence. (21st August 2003) - Dajani, Karma; Meester, Ronald
Abstract : We show that a cocycle, which is nothing but a generalized random walk with index setℤ d, with bounded step sizes is recurrent whenever its associated random entropy is zero, and transient whenever its associated random entropy is positive. This generalizes a well-known one-dimensional result and implies a Polya type dichotomy for this situation.