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SUMMARY:The Fyodorov-Bouchaud conjecture and Liouville conformal field the
 ory - Guillaume Remy (ENS Paris)
DTSTART:20180213T161500Z
DTEND:20180213T171500Z
UID:TALK93994@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:Starting from the restriction of a 2d Gaussian Free Field (GFF
 ) to the\nunit disk one can define a Gaussian multiplicative chaos (GMC) m
 easure\nwhose density is formally given by the exponential of the GFF. In 
 2008\nFyodorov and Bouchaud conjectured an exact formula for the density o
 f the\ntotal mass of this GMC. In this talk we will give a rigorous proof 
 of this\nformula. Our method is inspired by the technology developed by Ku
 piainen\,\nRhodes and Vargas to derive the DOZZ formula in the context of 
 Liouville\nconformal field theory on the Riemann sphere. The novel ingredi
 ents are\nthe study of the Liouville theory on Riemann surfaces with a bou
 ndary and\nthe key observations that the negative moments of the total mas
 s of GMC\ndetermine its law and are equal to one-point correlation functio
 ns of\nLiouville conformal field theory in the disk. Finally we will discu
 ss\napplications in random matrix theory\, asymptotics of the maximum of t
 he\nGFF\, and tail expansions of GMC.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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