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Exact formulas on Gaussian multiplicative chaos and Liouville theory

Presented by: 
Guillaume Remy CNRS - Ecole Normale Superieure Paris
Date: 
Friday 20th July 2018 - 09:10 to 09:55
Venue: 
INI Seminar Room 1
Abstract: 
We will present recent progress that has been made to prove exact formulas on the Gaussian multiplicative chaos (GMC) measures. We will give the law of the total mass of the GMC measure on the unit circle (the Fyodorov-Bouchaud formula) and on the unit interval (in collaboration with T. Zhu). The techniques of proof come from the link between GMC and Liouville conformal field theory studied by David-Kupiainen-Rhodes-Vargas. If time permits we will also discuss the connections with the quantum sphere and the quantum disk of the Duplantier-Miller-Sheffield approach to Liouville quantum gravity.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons