Di Patti, F, Azaele, S, Banavar, JR et al. (1 more author) (2011) System size expansion for systems with an absorbing state. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 83 (1). 010102. ISSN 1539-3755
Abstract
The well-known van Kampen system size expansion, while of rather general applicability, is shown to fail to reproduce some qualitative features of the time evolution for systems with an absorbing state, apart from a transient initial time interval. We generalize the van Kampen ansatz by introducing a new prescription leading to non-Gaussian fluctuations around the absorbing state. The two expansion predictions are explicitly compared for the infinite range voter model with speciation as a paradigmatic model with an absorbing state. The new expansion, both for a finite size system in the large time limit and at finite time in the large size limit, converges to the exact solution as obtained in a numerical implementation using the Gillespie algorithm. Furthermore, the predicted lifetime distribution is shown to have the correct asymptotic behavior.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | (c) 2011, American Physical Society. Reproduced in accordance with the publisher's self-archiving policy |
Keywords: | Models |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 21 May 2014 09:36 |
Last Modified: | 30 Jan 2018 09:48 |
Published Version: | http://dx.doi.org/10.1103/PhysRevE.83.010102 |
Status: | Published |
Publisher: | American Physical Society |
Identification Number: | 10.1103/PhysRevE.83.010102 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:78942 |