Probability distribution functions of sub- and super-diffusive systems

TL;DR

This paper investigates the probability distribution functions in systems exhibiting anomalous diffusion, including subdiffusive random walks on fractal lattices and superdiffusive driven Brownian particles, analyzing their scaling and universality properties.

Contribution

It introduces a comparative analysis of distribution functions in sub- and super-diffusive systems, highlighting the presence or absence of scaling and universality in their shapes.

Findings

Subdiffusive systems show non-universal distribution shapes.

Superdiffusive systems exhibit scaling behavior in distributions.

Distribution shapes depend on the type of anomalous transport.

Abstract

We study the anomalous transport in systems of random walks (RW's) on comb-like lattices with fractal sidebranches, showing subdiffusion, and in a system of Brownian particles driven by a random shear along the x-direction, showing a superdiffusive behavior. In particular, we discuss whether scaling and universality are present or not in the shapes of the particle distribution along the preferential transport direction (x-axis).