Second meeting
15-16 October 2026

Abstracts and titles to come

Abstracts and titles to come

Joakim Cronvall : A direct approach to soft and hard edge universality for random normal matrices.

Abstract: The random normal matrix model is a two-dimensional point process describing log-correlated particles in a confining field. The statistics are described by the reproducing kernel of a weighted polynomial Bergman space. Typically, one studies the kernel using asymptotics of orthogonal polynomials. In many interesting situations, such as when the eigenvalues are confined by a hard wall or when the eigenvalues concentrate on disconnected sets, this has turned out to be complicated. In this talk, I will discuss an alternative approach that altogether avoids orthogonal polynomials. Instead we work with Hilbert spaces of entire functions using Paley-Wiener type theorems and potential theory.  This approach gives several new universality results and shows in particular how the microscopic behavior of the kernel depends on the local potential theory.
Based on joint work with Aron Wennman