Diffusion regimes in Levy flights with trapping

TL;DR

This paper investigates how Levy flights with traps exhibit various diffusion behaviors depending on fluctuation magnitudes, using Levy stable distribution theory to characterize these regimes.

Contribution

It introduces a framework to classify diffusion regimes in Levy flights with trapping based on fluctuation magnitudes, avoiding divergence issues.

Findings

Different diffusion regimes identified based on fluctuation magnitudes.

A characterization of regimes using Levy stable distribution limit theorems.

Constant velocity assumption prevents divergence of mean squared displacement.

Abstract

The diffusion of a walk in the presence of traps is investigated. Different diffusion regimes are obtained considering the magnitude of the fluctuations in waiting times and jump distances. A constant velocity during the jump motion is assumed to avoid the divergence of the mean squared displacement. Using the limit theorems of the theory of Levy stable distributions we have provided a characterization of the different diffusion regimes.