Random zero sets for Fock type spaces

Abstract

Given a nondecreasing sequence $\Lambda =\{{\lambda }_n>0\}$ such that $\underset{n\to \infty }{\lim }{\lambda }_n=\infty ,$ we consider the sequence ${\mathcal{N}}_{\Lambda }:=\left\{{\lambda }_n{e}^{i{\theta }_n},n\in \mathbb{N}\right\}$, where ${\theta }_n$ are independent random variables uniformly distributed on $[0,2\pi ].$ We discuss the conditions on the sequence $\Lambda$ under which ${\mathcal{N}}_{\Lambda }$ is a zero set (a uniqness set) of a given weighted Fock space almost surely. The critical density of the sequence $\Lambda$ with respect to the weight is found.