Random entropy and recurrence

K. Dajani; R.W.J. Meester

doi:10.1155/s0161171203212217

Random entropy and recurrence

K. Dajani, R.W.J. Meester

Mathematics

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Abstract

We show that a cocycle, which is nothing but a generalized random walk with index set □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. Copyright © 2003 Hindawi Publishing Corporation. All rights reserved.

Original language	English
Pages (from-to)	2977-2988
Journal	International Journal of Mathematics and Mathematical Sciences
Issue number	47
DOIs	https://doi.org/10.1155/s0161171203212217
Publication status	Published - 2003

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MR2010744

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Random entropy and recurrence

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