THE NUMBER OF ENDS IN THE UNIFORM SPANNING TREE FOR RECURRENT UNIMODULAR RANDOM GRAPHS
成果类型：
Article
署名作者：
Van Engelenburg, Diederik; Hutchcroft, Tom
署名单位：
University of Vienna; California Institute of Technology
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/24-AOP1682
发表日期：
2024
页码：
2079-2103
关键词：
摘要：
We prove that if a unimodular random rooted graph is recurrent, the number of ends of its uniform spanning tree is almost surely equal to the number of ends of the graph. Together with previous results in the transient case, this completely resolves the problem of the number of ends of wired uniform spanning forest components in unimodular random rooted graphs and confirms a conjecture of Aldous and Lyons (2006).