Fastest First-Passage Time for Multiple Searchers with Finite Speed.

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.