Perfect Matchings as IID Factors on Non-Amenable Groups
Probability
2011-09-20 v3 Combinatorics
Dynamical Systems
Abstract
We prove that in every bipartite Cayley graph of every non-amenable group, there is a perfect matching that is obtained as a factor of independent uniform random variables. We also discuss expansion properties of factors and improve the Hoffman spectral bound on independence number of finite graphs.
Keywords
Cite
@article{arxiv.0911.0092,
title = {Perfect Matchings as IID Factors on Non-Amenable Groups},
author = {Russell Lyons and Fedor Nazarov},
journal= {arXiv preprint arXiv:0911.0092},
year = {2011}
}
Comments
16 pages; corrected missing reference in v2