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Seminars

Seminar
FIELD Math:Analysis
DATE December 15 (Tue), 2020
TIME 17:00-18:00
PLACE Online
SPEAKER Wennman, Aron
HOST Seo, Seong-Mi
INSTITUTE Tel Aviv University
TITLE The hole event for Gaussian complex zeros and the emergence of quadrature domains
ABSTRACT The Gaussian Entire Function (GEF) is a random Taylor series, whose zero set forms an invariant point process in the plane. We are interested in the zero distribution of the GEF, conditioned on the event that no zero lies in a given (large) region. For circular holes Ghosh and Nishry observed that as the radius of the hole tends to infinity, the density of zeros vanishes not only on the given hole, but also on an annulus beyond the (rescaled) hole ? a 'forbidden region' emerges.
In this talk 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 a curious emergence of quadrature domains.

Based on joint work with Alon Nishry.
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