title: Slow Lévy flights.
abstract: Among Markovian processes, the hallmark of Lévy flights is superdiffusion, or faster-than-Brownian dynamics. Here we show that Lévy laws, as well as Gaussian distributions, can also be the limit distributions of processes with long-range memory that exhibit very slow diffusion, logarithmic in time. These processes are path dependent and anomalous motion emerges from frequent relocations to already visited sites. We show how the central limit theorem is modified in this context, keeping the usual distinction between analytic and nonanalytic characteristic functions. A fluctuation-dissipation relation is also derived. Our results may have important applications in the study of animal and human displacements.
authors.affiliation: Instituto de Física, Universidad Nacional Autónoma de México, Distrito Federal 04510, Mexico.|Centro de Ciencias de la Complejidad, Universidad Nacional Autónoma de México, Distrito Federal 04510, Mexico.|Max-Planck-Institut für Physik Komplexer Systeme, Nöthnitzer Straße 38, D-01187 Dresden, Germany.
authors.forename: Denis
authors.initials: D
authors.lastname: Boyer
authors.affiliation: Instituto de Física, Universidad Nacional Autónoma de México, Distrito Federal 04510, Mexico.
authors.forename: Inti
authors.initials: I
authors.lastname: Pineda