Non-homogeneous persistent random walks and averaged environment for the L\'evy-Lorentz gas

TL;DR

This paper studies a non-homogeneous persistent random walk model, a mean-field version of the Le9vy-Lorentz gas, revealing a transition from normal diffusion to superdiffusion as the tail parameter varies.

Contribution

It introduces a continuum limit analysis of a non-homogeneous persistent random walk, highlighting the transition between diffusive regimes based on the tail parameter.

Findings

Transition from normal transport to superdiffusion with changing b5

Continuum limits characterize different transport regimes

Model captures effects of fat-tailed scatterer distributions

Abstract

We consider transport properties for a non-homogeneous persistent random walk, that may be viewed as a mean-field version of the L\'evy-Lorentz gas, namely a 1-d model characterized by a fat polynomial tail of the distribution of scatterers' distance, with parameter $\alpha$. By varying the value of $\alpha$ we have a transition from normal transport to superdiffusion, which we characterize by appropriate continuum limits.