Searching for clusters of targets under stochastic resetting

TL;DR

This paper analyzes how stochastic resetting affects the efficiency of searching for multiple targets in one-dimensional diffusion, revealing counterintuitive effects and optimal arrangements for target placement.

Contribution

It introduces a model for diffusion with stochastic resetting to find multiple targets and derives recursive formulas for mean search times, including optimal target configurations.

Findings

Increasing target distance can decrease search time.

Optimal target arrangements depend on limiting cases.

Recursive expressions for mean search times for multiple targets.

Abstract

We consider diffusion under stochastic resetting to the origin in one dimension and compute the mean time to find both of two targets placed either side of the origin. A surprising result is that increasing the distance between two targets can decrease the overall search time. We compute the optimal arrangement of two targets in limiting cases. We generalise to obtain recursive expressions for the mean time to find all of multiple targets. We discuss the relevance to real-world problems of locating multiple targets such as proteins locating clusters of DNA lesions.