Séminaire du 6 décembre 2010, 10h30: Marc
Lelarge, TREC, INRIA Paris-Rocquencourt & ENSP.
Matchings on infinite graphs
We consider the Boltzmann distribution with positive fugacity over the
matchings of a finite graph, and we establish its weak convergence as
the
underlying graph converges locally to an infinite graph with finite
branching
number. As a by-product, we obtain convergence of the scaled logarithm
of the
matching polynomial. By letting then the fugacity tend to infinity, we
obtain
a limit theorem for the asymptotic size of a maximum matching in the
graph
sequence. joint work with Charles Bordenave and Justin Salez.
Virginie Collette
Last modified: Mon Sep 20 14:24:06 CEST 2010