2023/11/29 by Daniel Campos, Campos, Daniel, Vicenç Méndez +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · Social Sciences · #Diffusion and Search Dynamics #Evolutionary Game Theory and Cooperation #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2311.17828
openalex publication_date 2023/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We explore the case of a group of random walkers looking for a target randomly located in space, such that the number of walkers is not constant but new ones can join the search, or those that are active can abandon it, with constant rates rb and rd, respectively. Exact analytical solutions are provided both for the fastest-first-passage time and for the collective search time required to reach the target, in the seminal case of Brownian walkers with rd=0. We prove that even for such a simplified situation there exists an optimal rate rb at which walkers should join the search to minimize the collective effort required to reach the target. We discuss how these results open a new line to understand the optimal regulation of cooperative random searches, e.g. for the case of biological foraging in social species.