Superdifusão de caminhadas markovianas e não-markovianas

Abstract

Random walks are tools used in statistical physics to quantitatively describe the evolution of dynamical systems. Such systems are ubiquitous in Nature and each system requires a unique approach. Models of the motion of biological organisms are constructed based on the randomness observed in search strategies. Markovian models attempt to faithfully reproduce the movement behavior of animals, for example the tendency to retain directional memory. Two independent markovian models are known that describe random searches. Correlated Random Walks (CRW) describe re-orientation events via a distribution of turning angles between successive steps. In contrast, a Lévy Walk (LW) uses a uniform turning angle distribution with a Power law tailed distribution for the step lengths. In this thesis, we introduce a new hybrid model called Correlated Lévy Walk (CLW). This model uses both a nonuniform turning angle distribution as well as a power Law tailed step length distribution. We apply this model to describe animal movement and discuss the statistical properties of such walks. In the second part of this thesis, we review an important class of stochastic non-Markovian processes, based on recent studies of walks with unlimited memory generated from a binary decision process with partial or complete recall of the history of the system.