Search and escape of mortal random walkers

TL;DR

This paper reviews first-passage problems involving mortal walkers with finite lifetimes, highlighting how mortality influences search efficiency and space exploration across various scenarios.

Contribution

It synthesizes recent results on mortal walkers, extending standard first-passage frameworks to include mortality effects in diverse physical and biological models.

Findings

Mortality drastically alters first-passage times.

Standard formalism can be adapted for mortal walkers.

Various scenarios like resetting and anomalous diffusion are analyzed.

Abstract

We review some representative results for first-passage problems involving so-called mortal or evanescent walkers, i.e., walkers with a finite lifetime. The mortality constraint plays a key role in the modeling of many real scenarios, as it filters out long Brownian trajectories, thereby drastically modifying space exploration properties. Among such scenarios, we consider here different first-passage problems, including one or many searchers, resetting, anomalous diffusion, evolving domains, and the narrow escape problem. In spite of the different physics, the mathematical treatment draws strongly on the formalism for standard (i.e., immortal) walkers.