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Random entropy and recurrence

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  • Karma Dajani
  • Ronald Meester

Abstract

We show that a cocycle, which is nothing but a generalized random walk with index set ℤ 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.

Suggested Citation

  • Karma Dajani & Ronald Meester, 2003. "Random entropy and recurrence," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-12, January.
    • Handle: RePEc:hin:jijmms:193967
    DOI: 10.1155/S0161171203212217
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