Scaling limits of L\'evy walks with random velocities

Hubert Woszczek; Marek A. Teuerle; Agnieszka Wyłomańska

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arXiv · 2604.23610

Scaling limits of L\'evy walks with random velocities

Hubert Woszczek·Marek A. Teuerle·Agnieszka Wyłomańska

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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.

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Hubert Woszczek, Marek A. Teuerle, Agnieszka Wyłomańska. 2026-04-26. Scaling limits of L\'evy walks with random velocities. https://arxiv.org/abs/2604.23610

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