Origin of universality in the onset of superdiffusion in Lévy walks

Abstract

Superdiffusion arises when complicated, correlated and noisy motion at the microscopic scale conspires to yield peculiar dynamics at the macroscopic scale. It ubiquitously appears in a variety of scenarios, spanning a broad range of scientific disciplines. The approach of superdiffusive systems towards their long-time, asymptotic behavior was recently studied using the Lévy walk of order $1<\beta <2$, revealing a universal transition at the critical ${\beta }_c=3/2$. Here, we investigate the origin of this transition and identify two crucial ingredients: a finite velocity which couples the walker's position to time and a corresponding transition in the fluctuations of the number of walks $n$ completed by the walker at time $t$.

arXiv comment6 pages with 4 figures and supplemental material

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• Anomalous diffusion and Lévy walks distinguish active from inertial turbulence