One-ended spanning trees in amenable unimodular graphs
Probability
2020-05-11 v1
Abstract
We prove that every amenable one-ended Cayley graph has an invariant spanning tree of one end. More generally, for any 1-ended amenable unimodular random graph we construct a factor of iid percolation (jointly unimodular subgraph) that is almost surely a spanning tree of one end. In [2] and [1] similar claims were proved, but the resulting spanning tree had 1 or 2 ends, and one had no control of which of these two options would be the case.
Cite
@article{arxiv.1805.10690,
title = {One-ended spanning trees in amenable unimodular graphs},
author = {Adam Timar},
journal= {arXiv preprint arXiv:1805.10690},
year = {2020}
}
Comments
10 pages, 3 figures