On multiple-particle continuous-time random walks
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 continuou...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2004-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/S1110757X04308065 |
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| Summary: | 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. |
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| ISSN: | 1110-757X 1687-0042 |