Asymptotic densities of planar Lévy walks: a nonisotropic case
Abstract
Lévy walks are a particular type of continuoustime random walks which results in a superdiffusive spreading of an initially localized packet. The original onedimensional model has a simple schematization that is based on starting a new unidirectional motion event either in the positive or in the negative direction. We consider twodimensional generalization of Lévy walks in the form of the socalled XYmodel. It describes a particle moving with a constant velocity along one of the four basic directions and randomly switching between them when starting a new motion event. We address the ballistic regime and derive solutions for the asymptotic density profiles. The solutions have a form of firstorder integrals which can be evaluated numerically. For specific values of parameters we derive an exact expression. The analytic results are in perfect agreement with the results of finitetime numerical samplings.
 Publication:

arXiv eprints
 Pub Date:
 July 2021
 arXiv:
 arXiv:2107.01951
 Bibcode:
 2021arXiv210701951B
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Mathematical Physics