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 |
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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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| _version_ | 1832547584023986176 |
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| author | Peter Becker-Kern Hans-Peter Scheffler |
| author_facet | Peter Becker-Kern Hans-Peter Scheffler |
| author_sort | Peter Becker-Kern |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-83b315224b844a4bb1a5b0e996cc4d77 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-83b315224b844a4bb1a5b0e996cc4d772025-02-03T06:44:14ZengWileyJournal of Applied Mathematics1110-757X1687-00422004-01-012004321323310.1155/S1110757X04308065On multiple-particle continuous-time random walksPeter Becker-Kern0Hans-Peter Scheffler1Fachbereich Mathematik, University of Dortmund, Dortmund 44221, GermanyFachbereich Mathematik, University of Dortmund, Dortmund 44221, GermanyScaling 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.http://dx.doi.org/10.1155/S1110757X04308065 |
| spellingShingle | Peter Becker-Kern Hans-Peter Scheffler On multiple-particle continuous-time random walks Journal of Applied Mathematics |
| title | On multiple-particle continuous-time random walks |
| title_full | On multiple-particle continuous-time random walks |
| title_fullStr | On multiple-particle continuous-time random walks |
| title_full_unstemmed | On multiple-particle continuous-time random walks |
| title_short | On multiple-particle continuous-time random walks |
| title_sort | on multiple particle continuous time random walks |
| url | http://dx.doi.org/10.1155/S1110757X04308065 |
| work_keys_str_mv | AT peterbeckerkern onmultipleparticlecontinuoustimerandomwalks AT hanspeterscheffler onmultipleparticlecontinuoustimerandomwalks |