  We consider a minimal model of persistent random searcher with short range
memory. We calculate exactly for such searcher the mean first-passage time to a
target in a bounded domain and find that it admits a non trivial minimum as
function of the persistence length. This reveals an optimal search strategy
which differs markedly from the simple ballistic motion obtained in the case of
Poisson distributed targets. Our results show that the distribution of targets
plays a crucial role in the random search problem. In particular, in the
biologically relevant cases of either a single target or regular patterns of
targets, we find that, in strong contrast with repeated statements in the
literature, persistent random walks with exponential distribution of excursion
lengths can minimize the search time, and in that sense perform better than any
Levy walk.
