Wired Cycle-Breaking Dynamics for Uniform Spanning Forests
Institute of Mathematical Statistics
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Hutchcroft, T. (2016). Wired Cycle-Breaking Dynamics for Uniform Spanning Forests. Ann. Probab., 44 (6), 3879-3892. https://doi.org/10.1214/15-AOP1063
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.
External DOI: https://doi.org/10.1214/15-AOP1063
This record's URL: https://www.repository.cam.ac.uk/handle/1810/283542