Wired cycle-breaking dynamics for uniform spanning forests

IF 2.1 1区数学 Q1 STATISTICS & PROBABILITY

Annals of Probability Pub Date : 2015-04-15 DOI:10.1214/15-AOP1063

Tom Hutchcroft

引用次数: 15

Abstract

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.

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均匀跨越森林的有线循环打破动力学

我们证明了有线均匀生成森林(WUSFWUSF)的每一个分量在每一个瞬态可逆随机图中几乎肯定是一端的，从而消除了先前结果所要求的有界度假设。我们推断出，在每个超临界高尔顿-沃森树中，WUSFWUSF的每个组分几乎都是一端的，回答了Benjamini, Lyons, Peres和Schramm [Ann]的问题。可能。29(2001)1-65]。我们的证明引入并利用了一组马尔可夫链，在这些马尔可夫链下，导向的WUSFWUSF是平稳的，我们称之为有线破环动力学。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annals of Probability 数学-统计学与概率论

CiteScore

4.60

自引率

8.70%

发文量

审稿时长

6-12 weeks

期刊介绍： The Annals of Probability publishes research papers in modern probability theory, its relations to other areas of mathematics, and its applications in the physical and biological sciences. Emphasis is on importance, interest, and originality – formal novelty and correctness are not sufficient for publication. The Annals will also publish authoritative review papers and surveys of areas in vigorous development.