## The Fyodorov-Bouchaud conjecture and Liouville conformal field theory

### With Guillaume Remy (ENS Paris)

# The Fyodorov-Bouchaud conjecture and Liouville conformal field theory

Starting from the restriction of a 2d Gaussian Free Field (GFF) to the

unit disk one can define a Gaussian multiplicative chaos (GMC) measure

whose density is formally given by the exponential of the GFF . In 2008

Fyodorov and Bouchaud conjectured an exact formula for 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 developed by Kupiainen,

Rhodes and Vargas to derive the DOZZ formula in the context of Liouville

conformal field theory on the Riemann sphere. The novel ingredients are

the study of the Liouville theory on Riemann surfaces with a boundary and

the key observations that the negative moments of the total mass of GMC

determine its law and are equal to one-point correlation functions of

Liouville conformal field theory in the disk. Finally we will discuss

applications in random matrix theory, asymptotics of the maximum of the

GFF , and tail expansions of GMC .

- Speaker: Guillaume Remy (ENS Paris)
- Tuesday 13 February 2018, 16:15–17:15
- Venue: MR12, CMS, Wilberforce Road, Cambridge, CB3 0WB.
- Series: Probability; organiser: Perla Sousi.