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November 2016 Wired cycle-breaking dynamics for uniform spanning forests
Tom Hutchcroft
Ann. Probab. 44(6): 3879-3892 (November 2016). DOI: 10.1214/15-AOP1063

Abstract

We prove that every component of the wired uniform spanning forest (${\mathsf{WUSF}}$) 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 ${\mathsf{WUSF}}$ is one-ended almost surely in every supercritical Galton–Watson tree, answering a question of Benjamini, Lyons, Peres and Schramm [Ann. Probab. 29 (2001) 1–65].

Our proof introduces and exploits a family of Markov chains under which the oriented ${\mathsf{WUSF}}$ is stationary, which we call the wired cycle-breaking dynamics.

Citation

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Tom Hutchcroft. "Wired cycle-breaking dynamics for uniform spanning forests." Ann. Probab. 44 (6) 3879 - 3892, November 2016. https://doi.org/10.1214/15-AOP1063

Information

Received: 1 April 2015; Revised: 1 September 2015; Published: November 2016
First available in Project Euclid: 14 November 2016

zbMATH: 1364.05062
MathSciNet: MR3572326
Digital Object Identifier: 10.1214/15-AOP1063

Subjects:
Primary: 60D05

Rights: Copyright © 2016 Institute of Mathematical Statistics

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Vol.44 • No. 6 • November 2016
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