Statistical matching theory
In this talk I will survey some results 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.
All concepts (including matchings) will be defined, and hopefully the talk will be accessible to any mathematician. This is joint work with various subsets of Miklós Abért, Péter E. Frenkel, Tamás Hubai and Gábor Kun.