Perfect Matchings as IID Factors on Non-Amenable Groups

Mathematics – Probability

Scientific paper

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16 pages; corrected missing reference in v2

Scientific paper

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.

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