title: Non-Gaussian propagator for elephant random walks.
abstract: For almost a decade the consensus has held that the random walk propagator for the elephant random walk (ERW) model is a Gaussian. Here we present strong numerical evidence that the propagator is, in general, non-Gaussian and, in fact, non-Lévy. Motivated by this surprising finding, we seek a second, non-Gaussian solution to the associated Fokker-Planck equation. We prove mathematically, by calculating the skewness, that the ERW Fokker-Planck equation has a non-Gaussian propagator for the superdiffusive regime. Finally, we discuss some unusual aspects of the propagator in the context of higher order terms needed in the Fokker-Planck equation.
authors.affiliation: Departamento de Física e Química, FCFRP, Universidade de São Paulo, 14040-903 Ribeirão Preto, SP, Brazil.
authors.forename: M A A
authors.initials: MA
authors.lastname: da Silva
authors.forename: J C
authors.initials: JC
authors.lastname: Cressoni
authors.forename: Gunter M
authors.initials: GM
authors.lastname: Schütz
authors.forename: G M
authors.initials: GM
authors.lastname: Viswanathan
authors.forename: Steffen
authors.initials: S
authors.lastname: Trimper