Lévy flights and random searches

In this work we discuss some recent contributions to the random search problem. Our analysis includes superdiffusive Lévy processes and correlated random walks in several regimes of target site density, mobility and revisitability. We present results in the context of mean-field-like and closed-form average calculations, as well as numerical simulations. We then consider random searches performed in regular lattices and lattices with defects, and we discuss a necessary criterion for distinguishing true superdiffusion from correlated random walk processes. We invoke energy considerations in relation to critical survival states on the edge of extinction, and we analyze the emergence of Lévy behavior in deterministic search walks. Finally, we comment on the random search problem in the context of biological foraging.