Let $0\leq\tau_{1}\leq\tau_{2}\leq\cdots\leq\tau_{m}\leq1$, originated from a uniform distribution. Let also $\epsilon,\delta\in\mathbb{R}$, and $d\in\mathbb{N}$. What is the probability of having more than $d$ adjacent $\tau_{i}$-s pairs that the distance between them is $\delta$, up to an error $\epsilon$ ? In this paper we are going to show how this untreated theoretical probabilistic problem arises naturally from the motivation of analyzing a simple asynchronous algorithm for detection of signals with a known frequency, using the novel technology of an event camera.

翻译：设 $0\leq\tau_{1}\leq\tau_{2}\leq\cdots\leq\tau_{m}\leq1$ 服从均匀分布。另设 $\epsilon,\delta\in\mathbb{R}$，$d\in\mathbb{N}$。求在误差 $\epsilon$ 范围内，存在超过 $d$ 对相邻 $\tau_{i}$ 且其间距为 $\delta$ 的概率？本文旨在展示这一未处理的概率理论问题如何自然地产生于对一种基于事件相机新型技术的简单异步算法进行动机分析，该算法用于检测已知频率信号。