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