Statistical physics of random searches

We apply the theory of random walks to quantitatively describe the general problem of how to search efficiently for randomly located objects that can only be detected in the limited vicinity of a searcher who typically has a finite degree of "free will" to move and search at will. We illustrate Levy flight search processes by comparison to Brownian random walks and discuss experimental observations of Levy flights in the special case of biologica l organisms that search for food sites. We review recent findings indicatin g that an inverse square probability density distribution P(l) similar to l (-2) of step lengths l can lead to optimal searches. Finally we survey the explanations put forth to account for these surprising findings.