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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Distribution of gaussian multiplicative chaos on t
he unit interval - Tunan Zhu (ENS - Paris)
DTSTART;TZID=Europe/London:20180720T141000
DTEND;TZID=Europe/London:20180720T143000
UID:TALK108352AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/108352
DESCRIPTION:Starting from a log-correlated field one can defin
e by a standard regularization technique the asso
ciated Gaussian multiplicative chaos (GMC) measure
with density formally given by the exponential
of the log-correlated field. Very recently exact f
ormulas have been obtained for specific GMC meas
ures. On the Riemann sphere a proof of the celeb
rated DOZZ formula has been given by Kupiainen-Rho
des-Vargas and for the GMC on the unit circle th
e Fyodorov-Bouchaud formula has been recently prov
en by Remy. In this talk we will present additio
nal results on GMC measures associated to a log-co
rrelated field on the unit interval [0\,1]. We w
ill \;present a very general formula for the r
eal moments of the total mass of GMC with log-si
ngularities in 0 and 1. This proves a set of conje
ctures given by Fyodorov\, Le Doussal\, Rosso an
d Ostrovsky. As a corollary\, this gives the distr
ibution of the total mass.

LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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