The forbidden region for random zeros: appearance of quadrature domains

Abstract: We consider the hole event for Gaussian complex zeros. As the size of the hole increases, the density of zeros vanishes, not just inside the hole, but also on a macroscopic region beyond the (rescaled) hole - a 'forbidden region' emerges. Surprisingly, the shape of this region is rigid under perturbations of the hole.

I will discuss the shape of the forbidden region for general simply connected holes. I plan to explain how to study the limiting zero density through a constrained variational problem, and touch upon a curious emergence of quadrature domains from potential theory.

probability

Audience: advanced learners

Bangalore Probability Seminar

Series comments: The link to zoom meeting can be found on the seminar's google calendar - www.isibang.ac.in/~d.yogesh/BPS.html