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Fastest First-Passage Time for Multiple Searchers with Finite Speed
Phys. Rev. Lett. 137, 127102 – Published 15 September, 2026
DOI: https://doi.org/10.1103/7q39-h9dv
Abstract
Deploying Brownian searchers reduces the mean search time for an immobile target merely by a factor . 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 . 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.