Michael Grinfeld
Bak-Sneppen-type models and rank-driven processes
Grinfeld, Michael; Knight, Philip A.; Wade, Andrew R.
Abstract
The Bak-Sneppen model is a well-known stochastic model of evolution that exhibits self-organized criticality; only a few analytical results have been established for it so far. We report a surprising connection between Bak-Sneppen-type models and more tractable Markov processes that evolve without any reference to an underlying topology. Specifically, we show that in the case of a large number of species, the long time behavior of the fitness profile in the Bak-Sneppen model can be replicated by a model with a purely rank-based update rule whose asymptotics can be studied rigorously.
Citation
Grinfeld, M., Knight, P. A., & Wade, A. R. (2011). Bak-Sneppen-type models and rank-driven processes. Physical review E: Statistical, nonlinear, and soft matter physics, 84(4), Article 041124. https://doi.org/10.1103/physreve.84.041124
Journal Article Type | Article |
---|---|
Publication Date | Oct 1, 2011 |
Deposit Date | Oct 4, 2012 |
Publicly Available Date | Mar 28, 2024 |
Journal | Physical review . E, Statistical, nonlinear, and soft matter physics |
Print ISSN | 1539-3755 |
Electronic ISSN | 1550-2376 |
Publisher | American Physical Society |
Peer Reviewed | Peer Reviewed |
Volume | 84 |
Issue | 4 |
Article Number | 041124 |
DOI | https://doi.org/10.1103/physreve.84.041124 |
Files
Accepted Journal Article
(492 Kb)
PDF
Copyright Statement
© 2011 American Physical Society
You might also like
Iterated-logarithm laws for convex hulls of random walks with drift
(2023)
Journal Article
Passage-times for partially-homogeneous reflected random walks on the quadrant
(2023)
Journal Article
Deposition, diffusion, and nucleation on an interval
(2022)
Journal Article
Cutpoints of non-homogeneous random walks
(2022)
Journal Article
Downloadable Citations
About Durham Research Online (DRO)
Administrator e-mail: dro.admin@durham.ac.uk
This application uses the following open-source libraries:
SheetJS Community Edition
Apache License Version 2.0 (http://www.apache.org/licenses/)
PDF.js
Apache License Version 2.0 (http://www.apache.org/licenses/)
Font Awesome
SIL OFL 1.1 (http://scripts.sil.org/OFL)
MIT License (http://opensource.org/licenses/mit-license.html)
CC BY 3.0 ( http://creativecommons.org/licenses/by/3.0/)
Powered by Worktribe © 2024
Advanced Search