L\'evy walks

TL;DR

Lévy walks are a type of random walk model that captures anomalously fast diffusion with finite velocity, providing insights into complex transport phenomena across various scientific fields.

Contribution

This review offers a comprehensive introduction to Lévy walks, surveys their diverse applications, and discusses recent advances and future perspectives.

Findings

Lévy walks model anomalously fast diffusion.

Applications span optics, chaos, cold atoms, biophysics, and behavioral science.

Recent studies highlight their significance in understanding complex transport processes.

Abstract

Random walk is a fundamental concept with applications ranging from quantum physics to econometrics. Remarkably, one specific model of random walks appears to be ubiquitous across many fields as a tool to analyze transport phenomena in which the dispersal process is faster than dictated by Brownian diffusion. The L\'{e}vy walk model combines two key features, the ability to generate anomalously fast diffusion and a finite velocity of a random walker. Recent results in optics, Hamiltonian chaos, cold atom dynamics, bio-physics, and behavioral science demonstrate that this particular type of random walks provides significant insight into complex transport phenomena. This review provides a self-consistent introduction to L\'{e}vy walks, surveys their existing applications, including latest advances, and outlines further perspectives.