Random entropy and recurrence (Q1415148)
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scientific article; zbMATH DE number 2012589
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Random entropy and recurrence |
scientific article; zbMATH DE number 2012589 |
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Random entropy and recurrence (English)
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3 December 2003
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Summary: We show that a cocycle, which is nothing but a generalized random walk with index set \(\mathbb{Z}^d\), 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.
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recurrent behavior
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generalized random walk
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random entropy
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Polya type dichotomy
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