WIRED CYCLE-BREAKING DYNAMICS FOR UNIFORM SPANNING FORESTS

• 成果类型: Article
• 署名作者: Hutchcroft, Tom
• 署名单位: University of British Columbia
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/15-AOP1063
• 发表日期: 2016
• 页码: 3879-3892
• 关键词: trees

摘要

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 [Ann. Probab. 29 (2001) 1-65]. 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.