Scaling limits of L\'evy walks with random velocities

TL;DR

This paper analyzes the scaling behavior of Levy walks with random velocities, revealing how heavy-tailed durations and velocities influence anomalous diffusion across three regimes.

Contribution

It extends classical Levy walk models by incorporating random velocities and derives new scaling limits for different regimes.

Findings

Identifies three distinct scaling regimes including a critical case with logarithmic corrections.

Shows diffusion behavior depends on the interplay between heavy-tailed duration and velocity distributions.

Provides a framework for modeling anomalous transport in heterogeneous systems.

Abstract

This paper investigates L\'evy walks with random velocities, extending classical models beyond constant speed assumptions. We derive scaling limits, demonstrating that diffusion depends on interplay between heavy-tailed duration and velocity distributions. Three distinct scaling regimes are identified, including a critical case with logarithmic corrections, offering a precise framework for modeling anomalous transport in heterogeneous systems.