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Lévy walks

V. Zaburdaev*, S. Denisov†, and J. Klafter‡

V. Zaburdaev*

  • Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, D-01187 Dresden, Germany

S. Denisov†

  • Institute of Physics, University of Augsburg, Universitätstrasse 1, D-86159 Augsburg, Germany, Lobachevsky State University, Gagarin Avenue 23, 603950 Nizhny Novgorod, Russia, and Sumy State University, Rimsky-Korsakov Street 2, 40007 Sumy, Ukraine

J. Klafter‡

  • School of Chemistry, Tel Aviv University, 69978 Tel Aviv, Israel

  • *vzaburd@pks.mpg.de
  • †sergey.denisov@physik.uni-augsburg.de
  • ‡klafter@post.tau.ac.il
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Rev. Mod. Phys. 87, 483 – Published 9 June, 2015

DOI: https://doi.org/10.1103/RevModPhys.87.483

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 Lévy-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, biophysics, and behavioral science demonstrate that this particular type of random walk provides significant insight into complex transport phenomena. This review gives a self-consistent introduction to Lévy walks, surveys their existing applications, including latest advances, and outlines further perspectives.

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Rev. Mod. Phys. 87, 483– Published 9 June, 2015
  • Received 16 September 2014

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