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zbMATH Open
Article . 2021
Data sources: zbMATH Open
Proceedings of the American Mathematical Society
Article . 2021 . Peer-reviewed
Data sources: Crossref
https://dx.doi.org/10.48550/ar...
Article . 2019
License: arXiv Non-Exclusive Distribution
Data sources: Datacite
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Infinite-step stationarity of rotor walk and the wired spanning forest

Authors: Chan, Swee Hong;

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

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 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).

14 pages. Following the suggestion of the anonymous referee, we add the proofs to Lemma 4.2 and Lemma 4.3. Other changes are minor

Related Organizations
Keywords

rotor-router, 05C81, 82C20 (Primary) 05C05 (Secondary), rotor walk, Probability (math.PR), Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics, uniform spanning forest, Trees, stationary distribution, wired spanning forest, Random walks on graphs, FOS: Mathematics, Mathematics - Combinatorics, escape rate., Combinatorics (math.CO), Mathematics - Probability

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
Average
Average
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bronze