Speaker:
Joakim Cronwall, Lund University
Abstract:
The correlation kernel of the random normal matrix model is the reproducing kernel of a polynomial subspace of a weighted L2-space. At the boundary of the droplet, the rescaled kernel converges to a certain universal error-function type kernel. This universality was proven by Hedenmalm and Wennman using an asymptotic formula for the orthogonal polynomials. I will discuss a new proof of the boundary universality and how this new method can be used to establish universality in the random normal matrix model with a soft/hard edge. Ongoing joint work with Aron Wennman.