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 < β < 2, revealing a universal transition at the critical β 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.

An update on passive transport in and out of plant cells

“…A recent development with a generalized Brownian but non-Gaussian model is presented in Sposini et al (2018) . The transition to superdiffusion, a > 1, has been studied using a Lévy process ( Miron, 2020 ) and is associated with active transport ( Reverey et al, 2015 ; Chechkin et al, 2017 ). Detailed descriptions of the physical ideas with the associated mathematics of stochastic models can be found in the excellent review by ( Bressloff and Newby, 2013 ).…”