Journal of Applied Mathematics
Volume 2004 (2004), Issue 3, Pages 213-233
doi:10.1155/S1110757X04308065
On multiple-particle continuous-time random walks
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.
Abstract
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.