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SUMMARY:Matchings and rank for random diluted graphs - Lelarge\, M (ENS)
DTSTART:20100325T140000Z
DTEND:20100325T150000Z
UID:TALK23837@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:We study matchings on a sequence of random graphs that converg
 e locally to trees. Inspired by techniques from random matrix theory\, we 
 rigorously prove the validity of the cavity method for the computation of 
 the entropy. At a positive temperature\, the cavity equations are interpre
 ted as equations for the local marginals of the Boltzmann Gibbs distributi
 on in the space of matchings on a (possibly) infinite tree. These equation
 s also appear in the computation of the asymptotic rank of the adjacency m
 atrices of the random graphs. We also define a determinantal process on th
 e tree which is the limit at positive temperature of the matchings on the 
 sequence of graphs. (joint work with Charles Bordenave and Justin Salez) 
LOCATION:Seminar Room 1\, Newton Institute
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