Qian Ai

A Functional Central Limit Theorem for Window Counts of Hardy--Szeg\H{o} Zeros

The Hardy--Szeg\H{o} zero process, investigated in the disk by Peres and Vir\'ag through the independent identically distributed Gaussian analytic function, is a canonical conformally invariant determinantal point process. This paper studies its upper half-plane realization. Although conformally equivalent to the disk...