title: Asymptotic densities of ballistic Lévy walks.
abstract: We propose an analytical method to determine the shape of density profiles in the asymptotic long-time limit for a broad class of coupled continuous-time random walks which operate in the ballistic regime. In particular, we show that different scenarios of performing a random-walk step, via making an instantaneous jump penalized by a proper waiting time or via moving with a constant speed, dramatically effect the corresponding propagators, despite the fact that the end points of the steps are identical. Furthermore, if the speed during each step of the random walk is itself a random variable, its distribution gets clearly reflected in the asymptotic density of random walkers. These features are in contrast with more standard nonballistic random walks.
authors.affiliation: Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, D-01187 Dresden, Germany.
authors.forename: D
authors.initials: D
authors.lastname: Froemberg
authors.affiliation: Insitut für Theoretische Physik 2: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, 40204 Düsseldorf, Germany.
authors.forename: M
authors.initials: M
authors.lastname: Schmiedeberg
authors.affiliation: Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan, 52900, Israel.
authors.forename: E
authors.initials: E
authors.lastname: Barkai
authors.affiliation: Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, D-01187 Dresden, Germany.
authors.forename: V
authors.initials: V
authors.lastname: Zaburdaev