Open Access
2023 Transience of simple random walks with linear entropy growth
Ben Morris, Hamilton Samraj Santhakumar
Author Affiliations +
Electron. Commun. Probab. 28: 1-8 (2023). DOI: 10.1214/23-ECP532

Abstract

Using the technique of evolving sets, we explore the connection between entropy growth and transience for simple random walks on connected infinite graphs with bounded degree. In particular we show that for a simple random walk starting at a vertex x0, if the entropy after n steps, En is at least Cn where the C is independent of x0, then the random walk is transient. We also give an example which demonstrates that the condition of C being independent of x0 is necessary.

Acknowledgments

We are grateful to Itai Benjamini for sharing this problem with us and we thank Gady Kozma for sharing the counterexample of Section 6.

Citation

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Ben Morris. Hamilton Samraj Santhakumar. "Transience of simple random walks with linear entropy growth." Electron. Commun. Probab. 28 1 - 8, 2023. https://doi.org/10.1214/23-ECP532

Information

Received: 13 February 2023; Accepted: 10 July 2023; Published: 2023
First available in Project Euclid: 19 July 2023

MathSciNet: MR4621594
zbMATH: 07734105
Digital Object Identifier: 10.1214/23-ECP532

Subjects:
Primary: 60J10

Keywords: Entropy , Simple random walk , transience

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