The fastest of N independent power-law-jump walkers reaches a target at distance X in time X/v + (⟨t⟩/N)(X/(v t0))^α, giving a 1/N speed-up over Brownian search with a crossover at α_c ~ 2 + ln N / ln(X/(v t0)).
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Rare Events and Redundancy in Random Walkers Target Search in a Finite Domain
The fastest of N independent power-law-jump walkers reaches a target at distance X in time X/v + (⟨t⟩/N)(X/(v t0))^α, giving a 1/N speed-up over Brownian search with a crossover at α_c ~ 2 + ln N / ln(X/(v t0)).