Random matrices and logarithmically correlated fields: dimensions 2 and 3

Paul Bourgade, NYU
Fine Hall 224

The Liouville quantum gravity measure is a properly normalized exponential of 2d log-correlated fields, such as the Gaussian free field. I will explain how this naturally appears in random matrix theory either in space time from random matrix dynamics, or in space from the characteristic polynomial of random normal matrices. A 3d log-correlated field also naturally emerges in random matrix theory, from dynamics on non-Hermitian matrices. This is based on works with Falconet, Dubach, Hartung, Cipolloni and Huang.