Friday 16th March 2018
Theodoros Assiotis | University of Warwick | Mathematics Institute
Howard House, 4th Floor Seminar Room

Determinantal structures in (2+1)-dimensional growth and decay models
I will talk about an inhomogeneous growth and decay model with a wall present in which the growth and decay rates on a single horizontal slice of the surface can be chosen essentially arbitrarily depending on the position. This model turns out to have a determinantal structure and most remarkably for a certain, the fully packed, initial condition the correlation kernel can be calculated explicitly in terms of one dimensional orthogonal polynomials on the positive half line and their orthogonality measures.

Friday 19th January 2018
Guillaume Remy | École Normale Supérieure, Paris (ENS)
Howard House, 4th Floor Seminar Room

The Fyodorov-Bouchaud formula and Liouville conformal field theory
Starting from the restriction of a 2d Gaussian free field (GFF) to the
unit circle 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. In our case the key
observation is that the negative moments of the total mass of GMC on the
circle determine its law and are equal to one-point correlation functions
of Liouville theory in the unit disk. Finally we will discuss applications
in random matrix theory, asymptotics of the maximum of the GFF, and tail
expansions of GMC.