Let \((r_n)_{n=1}^\infty \) be a non-decreasing sequence of radii in \((0, \infty )\), and let \((\theta _n)_{n=1}^\infty \) be a sequence of independent random arguments uniformly distributed in \([0, 2\pi )\). In this paper, we establish a new sufficient condition on the sequence \((r_n)_{n=1}^\infty \) under which \((r_ne^{i\theta _n})_{n=1}^\infty \) is almost surely a zero set for Fock spaces. The condition is in terms of the sum of two characteristics involving the counting function. The sharpness of this condition is discussed and examples are presented to illustrate it.

中文翻译：

---

随机零集 Fock 空间的充分条件

让\((r_n)_{n=1}^\infty \)是\((0, \infty )\)中半径的非递减序列，并让\((\theta _n)_{n= 1}^\infty \)是在\([0, 2\pi )\) 中均匀分布的独立随机参数序列。在本文中，我们在序列\((r_n)_{n=1}^\infty \)上建立了一个新的充分条件，其中\((r_ne^{i\theta _n})_{n=1}^ \infty \)几乎肯定是 Fock 空间的零集。条件是涉及计数功能的两个特征的总和。讨论了这种情况的尖锐性，并提供了一些例子来说明它。