Karma Dajani, Ronald Meester, "Random entropy and recurrence", International Journal of Mathematics and Mathematical Sciences, vol. 2003, Article ID 193967, 12 pages, 2003. https://doi.org/10.1155/S0161171203212217
Random entropy and recurrence
We show that a cocycle, which is nothing but a generalized random walk with index set , 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.
Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.