generalized random walk
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scholarly journals Random entropy and recurrence

2003 ◽  
Vol 2003 (47) ◽  
pp. 2977-2988
Author(s):  
Karma Dajani ◽  
Ronald Meester
Keyword(s):  
Random Walk ◽  
Index Set ◽  
One Dimensional ◽  
Generalized Random Walk

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

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