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Distribution of gaussian multiplicative chaos on the unit interval

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RGMW06 - RGM follow up

Starting from a log-correlated field one can define by a standard 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 specific GMC measures. On the Riemann sphere a proof of the celebrated DOZZ 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 associated to a log-correlated field on the unit interval [0,1]. We will present a very general formula for the real moments of the total mass of GMC with log-singularities in 0 and 1. This proves a set of conjectures given by Fyodorov, Le Doussal, Rosso and Ostrovsky. As a corollary, this gives the distribution of the total mass.




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