Zeros of the i.i.d. Gaussian Laurent series on an annulus: weighted Szegő kernels and permanental-determinantal point processes

Makoto Katori, Tomoyuki Shirai

On an annulus ${\mathbb{A}}_q:=\{z\in \mathbb{C}:q<|z|<1\}$ with a fixed $q\in (0,1)$, we study a Gaussian analytic function (GAF) and its zero set which defines a point…