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Fastest First-Passage Time for Multiple Searchers with Finite Speed

Denis S. Grebenkov1, Ralf Metzler2, and Gleb Oshanin3

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Phys. Rev. Lett. 137, 127102 – Published 15 September, 2026

DOI: https://doi.org/10.1103/7q39-h9dv

Abstract

Deploying N Brownian searchers reduces the mean search time for an immobile target merely by a factor 1/lnN. We show that this conclusion is highly sensitive to the short-time dynamics of individual searchers. Based on the telegrapher’s equation we demonstrate that the classical logarithmic scaling is only an intermediate asymptotic and ultimately crosses over to a much faster exponential decay with N. For anomalous diffusion with finite speed, we also show that superdiffusion leads to faster search than subdiffusion, as intuitively expected. Our findings provide a clear physical picture of redundancy and minimal search times in collective search relevant for many biological and physical systems.

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Outline

Information

Phys. Rev. Lett. 137, 127102– Published 15 September, 2026
  • Received 17 February 2026
  • Accepted 3 August 2026
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