Asymptotic densities of ballistic Lévy walks

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
D FroembergV Zaburdaev

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.

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Citations

Oct 16, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Marco DentzFelipe P J de Barros
Sep 15, 2016·Physical Review. E·Marcin Magdziarz, Tomasz Zorawik
Mar 17, 2017·Physical Review. E·Marcin Magdziarz, Tomasz Zorawik
Jun 18, 2017·Physical Review. E·Bartłomiej DybiecAlexander A Dubkov
Jan 14, 2017·Physical Review Letters·V ZaburdaevE Barkai
Jan 20, 2018·Physical Review. E·A Kamińska, T Srokowski
Jan 20, 2018·Physical Review. E·Helena Stage
Sep 28, 2017·Physical Review. E·Daxing XiongEli Barkai
Mar 18, 2016·Physical Review. E·Sergei Fedotov
Dec 18, 2020·Physical Review. E·Wanli WangEli Barkai

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