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SUMMARY:Distribution of gaussian multiplicative chaos on the unit interval
  - Tunan Zhu (ENS - Paris)
DTSTART:20180720T131000Z
DTEND:20180720T133000Z
UID:TALK108352@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Starting from a log-correlated field one can define by a stand
 ard regularization  technique the associated Gaussian multiplicative chaos
  (GMC) measure with density   formally given by the exponential of the log
 -correlated field. Very recently exact formulas   have been obtained for s
 pecific GMC measures. On the Riemann sphere a proof of the   celebrated DO
 ZZ formula has been given by Kupiainen-Rhodes-Vargas and for the GMC   on 
 the unit circle the Fyodorov-Bouchaud formula has been recently proven by 
 Remy. In   this talk we will present additional results on GMC measures as
 sociated to a log-correlated   field on the unit interval [0\,1]. We will&
 nbsp\;present a very general formula for the real moments   of the total m
 ass of GMC with log-singularities in 0 and 1. This proves a set of conject
 ures   given by Fyodorov\, Le Doussal\, Rosso and Ostrovsky. As a corollar
 y\, this gives the distribution   of the total mass.  <br><br><br><br><br>
LOCATION:Seminar Room 1\, Newton Institute
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