Competition of many searchers

TL;DR

This paper reviews recent findings on the distribution of the fastest first passage times among many searchers, highlighting how these extreme times depend on search modes, initial conditions, and spatial domain properties.

Contribution

It provides a comprehensive review of the latest results on fastest first passage times, emphasizing their dependence on search dynamics and initial configurations.

Findings

Fastest FPTs vary significantly with search mode (diffusion, subdiffusion, superdiffusion, jumps).

Initial searcher distribution influences the extreme search times.

Spatial domain properties affect the distribution of fastest FPTs.

Abstract

First passage times (FPTs) are often used to study timescales in physical, chemical, and biological processes. FPTs generically describe the time it takes a random "searcher" to find a "target." In many systems, the important timescale is not the time it takes a single searcher to find a target, but rather the time it takes the fastest searcher out of many searchers to find a target. Such fastest FPTs or extreme FPTs result from many searchers competing to find the target and differ markedly from FPTs of single searchers. In this chapter, we review recent results on fastest FPTs. We show how fastest FPTs depend on the mode of stochastic search (including search by diffusion, subdiffusion, superdiffusion, and discrete jumps), the initial searcher distribution, and properties of the spatial domain.