
arXiv: 1909.13195
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
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
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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