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Updated: Oct 4, 2026

High Speed Sub-GHz Spectrometer for Brillouin Scattering Analysis
Published on: December 22, 2015
Fastest First-Passage Time for Multiple Searchers with Finite Speed
Denis S Grebenkov1, Ralf Metzler2, Gleb Oshanin3
1Ecole Polytechnique, CNRS, Laboratoire de Physique de la Matière Condensée, (UMR 7643), -, IP Paris, 91120 Palaiseau, France.
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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