Given a nondecreasing sequence $\Lambda=\{ \lambda_n>0\}$ such that $\displaystyle\lim_{ n\to\infty} \lambda_n=\infty,$ 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.
Categories: math.CV math.PR