Journal of Applied Mathematics
Volume 2004 (2004), Issue 3, Pages 213-233

On multiple-particle continuous-time random walks

Peter Becker-Kern and Hans-Peter Scheffler

Fachbereich Mathematik, University of Dortmund, Dortmund 44221, Germany

Received 18 August 2003; Revised 24 February 2004

Copyright © 2004 Peter Becker-Kern and Hans-Peter Scheffler. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Scaling limits of continuous-time random walks are used in physics to model anomalous diffusion in which particles spread at a different rate than the classical Brownian motion. In this paper, we characterize the scaling limit of the average of multiple particles, independently moving as a continuous-time random walk. The limit is taken by increasing the number of particles and scaling from microscopic to macroscopic view. We show that the limit is independent of the order of these limiting procedures and can also be taken simultaneously in both procedures. Whereas the scaling limit of a single-particle movement has quite an obscure behavior, the multiple-particle analogue has much nicer properties.