Caminhadas de Lévy dentro de cascas esféricas com fronteiras absorventes

Abstract

The Lévy Flight Foraging Hypothesis proposes that organisms have evolved to use Lévy walks as an e ective exploration strategy. There is substantial evidence in the literature supporting the notion that Lévy inverse square walks are optimal for foraging with revisits, regardless of dimensionality. However, more rigorous mathematical demonstrations of this phenomenon are still needed, especially for dimensions higher than 2. We investigate the foraging problem by considering the simpler case of concentric annuli or spherical shells, which is closely related to the full problem. By analyzing this approach, we show that Lévy inverse square walks are the optimal search strategy in the limit of foraging with revisits. This result is a strong evidence supporting the Lévy Flight Foraging Hypothesis in dimensions greater than 1.