Random zero sets for Fock type spaces

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