Gaultier Lambert: Applications of the theory of Gaussian multiplicative chaos to random matrices

Tid: Ti 2019-02-19 kl 15.15 - 16.15

Föreläsare: Gaultier Lambert

Plats: Room F11 KTH

Log–correlated fields are a class of stochastic processes which describe the fluctuations of some key observables in different probabilistic models in dimension 1 and 2. For instance in percolation theory, random domino tilings or the characteristic polynomials of random matrices.
Gaussian multiplicative chaos is a renormalization procedure which aims at defining the exponential of a Log–correlated field in the form of a family of random measures.
These random measures can be thought of as describing the extreme values of the underlying field. In this talk, we shall present some applications of the theory to study the logarithm of the characteristic polynomial of some random matrices, this will include the Gaussian unitary ensemble, circular beta ensembles and the Ginibre ensemble.