Entropy of random walk range

Itai Benjamini; Gady Kozma; Ariel Yadin; Amir Yehudayoff

doi:10.1214/09-AIHP345

Entropy of random walk range

Itai Benjamini, Gady Kozma, Ariel Yadin, Amir Yehudayoff

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

We study the entropy of the set traced by an n-step simple symmetric random walk on ℤ^d . We show that for d ≥ 3, the entropy is of order n. For d = 2, the entropy is of order n/ log² n. These values are essentially governed by the size of the boundary of the trace.

Original language	English
Pages (from-to)	1080-1092
Number of pages	13
Journal	Annales de l'institut Henri Poincare (B) Probability and Statistics
Volume	46
Issue number	4
DOIs	https://doi.org/10.1214/09-AIHP345
State	Published - 1 Nov 2010
Externally published	Yes

Keywords

Entropy
Random walk

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/09-AIHP345

Cite this

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abstract = "We study the entropy of the set traced by an n-step simple symmetric random walk on ℤd . We show that for d ≥ 3, the entropy is of order n. For d = 2, the entropy is of order n/ log2 n. These values are essentially governed by the size of the boundary of the trace.",

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AU - Kozma, Gady

AU - Yadin, Ariel

AU - Yehudayoff, Amir

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Y1 - 2010/11/1

N2 - We study the entropy of the set traced by an n-step simple symmetric random walk on ℤd . We show that for d ≥ 3, the entropy is of order n. For d = 2, the entropy is of order n/ log2 n. These values are essentially governed by the size of the boundary of the trace.

AB - We study the entropy of the set traced by an n-step simple symmetric random walk on ℤd . We show that for d ≥ 3, the entropy is of order n. For d = 2, the entropy is of order n/ log2 n. These values are essentially governed by the size of the boundary of the trace.

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M3 - Article

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Entropy of random walk range

Abstract

Keywords

ASJC Scopus subject areas

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