Random zero sets for Fock type spaces

Abstract

Given a nondecreasing sequence \(\Lambda =\{\lambda _n>0\}\) such that \(\displaystyle \lim _{n\rightarrow \infty } \lambda _n=\infty ,\) we consider the sequence \(\mathcal {N}_\Lambda :=\left\{ \lambda _ne^{i\theta _n},n\in \,\mathbb {N}\right\} \), 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.