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arXiv · 1510.05614

Explicit Densities of Multidimensional Lévy Walks

Marcin Magdziarz·Tomasz Zorawik
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Abstract

We provide explicit formulas for asymptotic densities of the 2- and 3-dimensional ballistic Lévy walks. It turns out that in the 3D case the densities are given by elementary functions. The densities of the 2D Lévy walks are expressed in terms of hypergeometric functions and the right-side Riemann-Liouville fractional derivative which allows to efficiently evaluate them numerically. The theoretical results agree with Monte-Carlo simulations. The obtained functions solve certain differential equations with the fractional material derivative.

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Marcin Magdziarz, Tomasz Zorawik. 2015-12-11. Explicit Densities of Multidimensional Lévy Walks. https://doi.org/10.1103/physreve.94.022130

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