Perfect matchings as IID factors on non-amenable groups

Authors:
Russell Lyons;Fedor Nazarov
Affiliations:
Department of Mathematics, 831 E. 3rd St., Indiana University, Bloomington, IN 47405-5701, United States;Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, WI 53706, United States
Venue:
European Journal of Combinatorics
Year:
2011

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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 the independence number of finite graphs.