Many physical, chemical, and biological systems depend on the first passage time (FPT) of a diffusive searcher to a target. Typically, this FPT is much slower than the characteristic diffusion timescale. For example, this is the case if the target is small (the narrow escape problem) or if the searcher must escape a potential well. However, many systems depend on the first time a searcher finds the target out of a large group of searchers, which is the so-called extreme FPT. Since this extreme FPT vanishes in the limit of many searchers, the prohibitively slow FPTs of diffusive search can be negated by deploying enough searchers. However, the notion of ‘enough searchers’ is poorly understood. How can one determine if a system is in the slow regime (dominated by small targets or a deep potential, for example) or the fast regime (dominated by many searchers)? How can one estimate the extreme FPT in these different regimes? In this paper, we answer these questions by deriving condi...

中文翻译：

---

慢速和快速模式之间的竞争，以实现极端的首次扩散时间

许多物理，化学和生物系统都取决于扩散搜索者到目标的第一次通过时间（FPT）。通常，此FPT比特征扩散时间尺度慢得多​​。例如，如果目标很小（逃生问题狭窄），或者搜索者必须逃脱一口潜在的井，就属于这种情况。但是，许多系统都依赖于搜索者第一次从大量搜索者中找到目标，这就是所谓的极限FPT。由于这种极端的FPT在许多搜索者的限制中消失了，因此可以通过部署足够的搜索者来消除扩散搜索的速度过慢的FPT。但是，对“足够的搜索者”的概念了解甚少。如何确定系统是否处于慢速状态（由小目标或深潜势所主导，例如）还是快速政权（由许多搜索者主导）？在这些不同的制度下，如何估算极端FPT？在本文中，我们通过得出条件来回答这些问题。