Perfect matchings as IID factors on non-amenable groups

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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. © 2011 Elsevier Ltd.

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Lyons, R., & Nazarov, F. (2011). Perfect matchings as IID factors on non-amenable groups. European Journal of Combinatorics, 32(7), 1115–1125. https://doi.org/10.1016/j.ejc.2011.03.008

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