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.
@article{arxiv.2604.23610,
title = {Scaling limits of L\'evy walks with random velocities},
author = {Hubert Woszczek and Marek A. Teuerle and Agnieszka Wyłomańska},
journal= {arXiv preprint arXiv:2604.23610},
year = {2026}
}