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SUMMARY:The Fyodorov-Bouchaud formula and Liouville conformal field theory
DTSTART:20180419T151500
DTEND:20180419T161500
DTSTAMP:20260501T072751Z
UID:b8f186a211508ead345e88d0daf7024957e06760e36b52757fd2c1aa
CATEGORIES:Conferences - Seminars
DESCRIPTION:Guillaume Rémy\nStarting from the restriction of a 2d Gaussia
 n free field (GFF) to the unit circle one can define a Gaussian multiplica
 tive chaos (GMC) measure whose density is formally given by the exponentia
 l of the GFF. In 2008 Fyodorov and Bouchaud conjectured an exact formula f
 or the density of the total mass of this GMC. In this talk we will give a 
 rigorous proof of this formula. Our method is inspired by the technology d
 eveloped by Kupiainen\, Rhodes and Vargas to derive the DOZZ formula in th
 e context of Liouville conformal field theory on the Riemann sphere. In ou
 r case the key observation is that the negative moments of the total mass 
 of GMC on the circle determine its law and are equal to one-point correlat
 ion functions of Liouville theory in the unit disk. Finally we will discus
 s applications in random matrix theory\, asymptotics of the maximum of the
  GFF\, and tail expansions of GMC.
LOCATION:MA B1 524 https://plan.epfl.ch/?room=MAB1524
STATUS:CONFIRMED
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