title: Random walks with preferential relocations to places visited in the past and their application to biology.
abstract: Strongly non-Markovian random walks offer a promising modeling framework for understanding animal and human mobility, yet, few analytical results are available for these processes. Here we solve exactly a model with long range memory where a random walker intermittently revisits previously visited sites according to a reinforced rule. The emergence of frequently visited locations generates very slow diffusion, logarithmic in time, whereas the walker probability density tends to a Gaussian. This scaling form does not emerge from the central limit theorem but from an unusual balance between random and long-range memory steps. In single trajectories, occupation patterns are heterogeneous and have a scale-free structure. The model exhibits good agreement with data of free-ranging capuchin monkeys.
authors.affiliation: Instituto de Física, Universidad Nacional Autónoma de México, Distrito Federal 04510, Mexico and Centro de Ciencias de la Complejidad, Universidad Nacional Autónoma de México, Distrito Federal 04510, Mexico.
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: Citlali
authors.initials: C
authors.lastname: Solis-Salas
mesh_terms: D000465:Algorithms; D000818:Animals; D001519:Behavior / Q000502:physiology*; D002428:Cebus; D006801:Humans; D008568:Memory / Q000502:physiology*; D008954:Models, Biological; D009068:Movement / Q000502:physiology*