Wired cycle-breaking dynamics for uniform spanning forests

Tom Hutchcroft ^[1]
1. [1] University of British Columbia
  
  University of British Columbia
  
  Canadá
Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 44, Nº. 6, 2016, págs. 3879-3892
Idioma: inglés
DOI: 10.1214/15-aop1063
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Resumen
- We prove that every component of the wired uniform spanning forest (WUSFWUSF) 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 WUSFWUSF 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 WUSFWUSF is stationary, which we call the wired cycle-breaking dynamics.