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arXiv · 1504.03928

Wired Cycle-Breaking Dynamics for Uniform Spanning Forests

Tom Hutchcroft
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Abstract

We prove that every component of the wired uniform spanning forest (WUSF) is one-ended almost surely in every transient reversible random graph, removing the bounded degree hypothesis required by earlier results. We deduce that every component of the WUSF is one-ended almost surely in every supercritical Galton-Watson tree, answering a question of Benjamini, Lyons, Peres and Schramm. Our proof introduces and exploits a family of Markov chains under which the oriented WUSF is stationary, which we call the wired cycle-breaking dynamics.

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Tom Hutchcroft. 2015-04-15. Wired Cycle-Breaking Dynamics for Uniform Spanning Forests. https://doi.org/10.1214/15-aop1063

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