Minor-excluded graphs and soficity
Combinatorics
2025-10-14 v2 Group Theory
Logic
Probability
Abstract
A random rooted graph is said to be sofic if it is the Benjamini-Schramm limit of a sequence of finite graphs. Given any finite graph , we prove that every one-ended, unimodular random rooted graph that does not have H as a minor must be sofic. The hypothesis regarding the number of ends can be dropped under the additional assumption that the graph is quasi-transitive.
Keywords
Cite
@article{arxiv.2508.06731,
title = {Minor-excluded graphs and soficity},
author = {Oriol Solé-Pi},
journal= {arXiv preprint arXiv:2508.06731},
year = {2025}
}
Comments
37 pages, 10 figures. Version 2: Minor improvements