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Infinite-step stationarity of rotor walk and the wired spanning forest


Author: Swee Hong Chan
Journal: Proc. Amer. Math. Soc. 149 (2021), 2415-2428
MSC (2020): Primary 05C81, 82C20; Secondary 05C05
DOI: https://doi.org/10.1090/proc/15476
Published electronically: March 26, 2021
MathSciNet review: 4246794
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Abstract: We study rotor walk, a deterministic counterpart of the simple random walk, on infinite transient graphs. We show that the final rotor configuration of the rotor walk (after the walker escapes to infinity) follows the law of the wired uniform spanning forest oriented toward infinity (OWUSF) measure when the initial rotor configuration is sampled from OWUSF. This result holds for all graphs for which each tree in the wired spanning forest has one single end almost surely. This answers a question posed in a previous work of the author (Chan 2018).


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Additional Information

Swee Hong Chan
Affiliation: Department of Mathematics, UCLA, Los Angeles, California 90095
MR Author ID: 1058757
ORCID: 0000-0003-0599-9901
Email: sweehong@math.ucla.edu

Keywords: Rotor walk, rotor-router, uniform spanning forest, wired spanning forest, stationary distribution, escape rate.
Received by editor(s): January 6, 2020
Received by editor(s) in revised form: November 20, 2020
Published electronically: March 26, 2021
Additional Notes: The author was supported in part by NSF grant DMS-1455272.
Communicated by: David Levin
Article copyright: © Copyright 2021 American Mathematical Society