The number of ends in the uniform spanning tree for recurrent unimodular random graphs
Probability
2023-01-11 v1
Abstract
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).
Keywords
Cite
@article{arxiv.2301.03875,
title = {The number of ends in the uniform spanning tree for recurrent unimodular random graphs},
author = {Diederik van Engelenburg and Tom Hutchcroft},
journal= {arXiv preprint arXiv:2301.03875},
year = {2023}
}
Comments
27 pages, comments are welcome