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 , if the entropy after n steps, is at least where the C is independent of , then the random walk is transient. We also give an example which demonstrates that the condition of C being independent of 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
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
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