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Statistical matching theory with a glimpse towards extremal regular graphs

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SNAW01 - Graph limits and statistics

In this talk we will survey some recent development on statistical properties of matchings of very large and infinite graphs. The main goal of the talk is to describe a few applications of a new concept called matching measure. These applications include new results on the number of (perfect) matchings in large girth graphs as well as simple new proofs of certain statistical physical theorems. In particular, we will sketch a new proof of Schrijver's lower bound for the number of perfect matchings of regular bipartite graphs. We will also mention some extremal graph theoretic results about other graph parameters of regular graphs.

This talk is based on joint papers with various subsets of Miklos Abert, Peter E. Frenkel, Tamas Hubai and Gabor Kun.

This talk is part of the Isaac Newton Institute Seminar Series series.

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