Dynamic redundancy as a mechanism to optimize collective random searches

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Abstract

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 time cost required to reach the target, for the exemplifying case of Brownian walkers with rd=0. We prove that even for such a simple situation there exists an optimal rate rb at which walkers should join the search to minimize the collective search costs. We discuss how these results open a new line to understand the optimal regulation in searches conducted through multiparticle random walks, e.g., in chemical or biological processes.

Original languageEnglish
Article number064109
Number of pages6
JournalPhysical Review E
Volume109
Issue number6
DOIs
Publication statusPublished - 3 Jun 2024

Keywords

  • 1st passage times
  • Order-statistics
  • Random walkers
  • Diffusion
  • Memory

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