论文标题
慢速和快速制度之间的竞争，以实现极端传递时间的扩散时间
Competition between slow and fast regimes for extreme first passage times of diffusion
论文作者
论文摘要
许多物理，化学和生物系统取决于扩散搜索者到目标的第一个通过时间（FPT）。通常，此FPT比特征扩散时间尺度要慢得多。例如，如果目标很小（狭窄的逃生问题），或者搜索者必须逃脱潜在的井。但是，许多系统取决于搜索者第一次从一大批搜索者中找到目标，这是所谓的极端fpt。由于这种极端的FPT在许多搜索者的限制中消失了，因此通过部署足够的搜索者可以否定扩散搜索的慢速FPT。但是，“足够的搜索者”的概念知之甚少。如何确定系统是否处于缓慢的状态（例如，由小目标或深度电位主导）或快速制度（由许多搜索者主导）？在这些不同的制度中，如何估计极端FPT？在本文中，我们通过得出条件来回答这些问题，这些条件确保系统处于政权状态，并在这些制度中找到完整分布和极端FPT的所有时刻。我们的分析表明，初始搜索者分布和目标反应性可以对极端FPT产生的关键效果。
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 conditions which ensure that a system is in either regime and finding approximations of the full distribution and all the moments of the extreme FPT in these regimes. Our analysis reveals the critical effect that initial searcher distribution and target reactivity can have on extreme FPTs.
