Open Access
April 2008 Renormalization of the two-dimensional Lotka–Volterra model
J. Theodore Cox, Edwin A. Perkins
Ann. Appl. Probab. 18(2): 747-812 (April 2008). DOI: 10.1214/07-AAP453

Abstract

We show that renormalized two-dimensional Lotka–Volterra models near criticality converge to a super-Brownian motion. This is used to establish long-term survival of a rare type for a range of parameter values near the voter model.

Citation

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J. Theodore Cox. Edwin A. Perkins. "Renormalization of the two-dimensional Lotka–Volterra model." Ann. Appl. Probab. 18 (2) 747 - 812, April 2008. https://doi.org/10.1214/07-AAP453

Information

Published: April 2008
First available in Project Euclid: 20 March 2008

zbMATH: 1141.60060
MathSciNet: MR2399711
Digital Object Identifier: 10.1214/07-AAP453

Subjects:
Primary: 60G57 , 60K35
Secondary: 60F17 , 60J80

Keywords: Lotka–Volterra model , Super-Brownian motion , voter model

Rights: Copyright © 2008 Institute of Mathematical Statistics

Vol.18 • No. 2 • April 2008
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