Extreme Statistics of Superdiffusive Lévy Flights and Every Other Lévy Subordinate Brownian Motion

The search for hidden targets is a fundamental problem in many areas of science, engineering, and other fields. Studies processes often adopt probabilistic framework, which searcher randomly explores spatial domain located target. There has been significant interest controversy regarding optimal strategies, especially superdiffusive processes. strategy typically defined as the that minimizes time it takes given single to find target, called first hitting (FHT). However, systems involve multiple searchers, important timescale fastest an extreme FHT. In this paper, we study FHTs any stochastic process random change Brownian motion by Lévy subordinator. This class includes flights space dimension, are described Fokker–Planck equation with fractional Laplacian. We short-time distribution FHT subordinate use full moments number searchers grows. illustrate these rigorous results several examples numerical simulations.