Factor-of-iid balanced orientation of non-amenable graphs
Probability
2023-08-15 v1 Combinatorics
Dynamical Systems
Abstract
We show that if a non-amenable, quasi-transitive, unimodular graph has all degrees even then it has a factor-of-iid balanced orientation, meaning each vertex has equal in- and outdegree. This result involves extending earlier spectral-theoretic results on Bernoulli shifts to the Bernoulli graphings of quasi-transitive, unimodular graphs. As a consequence, we also obtain that when is regular (of either odd or even degree) and bipartite, it has a factor-of-iid perfect matching. This generalizes a result of Lyons and Nazarov beyond transitive graphs.
Keywords
Cite
@article{arxiv.2106.12530,
title = {Factor-of-iid balanced orientation of non-amenable graphs},
author = {Ferenc Bencs and Aranka Hrušková and László Márton Tóth},
journal= {arXiv preprint arXiv:2106.12530},
year = {2023}
}
Comments
24 pages, 1 figure. This is one of two papers that are replacing the shorter arXiv submission arXiv:2101.12577v1 Factor of iid Schreier decoration of transitive graphs