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2010 Coexistence in a Two-Dimensional Lotka-Volterra Model
J. Theodore Cox, Mathieu Merle, Edwin Perkins
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Electron. J. Probab. 15: 1190-1266 (2010). DOI: 10.1214/EJP.v15-795

Abstract

We study the stochastic spatial model for competing species introduced by Neuhauser and Pacala in two spatial dimensions. In particular we confirm a conjecture of theirs by showing that there is coexistence of types when the competition parameters between types are equal and less than, and close to, the within types parameter. In fact coexistence is established on a thorn-shaped region in parameter space including the above piece of the diagonal. The result is delicate since coex- istence fails for the two-dimensional voter model which corresponds to the tip of the thorn. The proof uses a convergence theorem showing that a rescaled process converges to super-Brownian motion even when the parameters converge to those of the voter model at a very slow rate.

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J. Theodore Cox. Mathieu Merle. Edwin Perkins. "Coexistence in a Two-Dimensional Lotka-Volterra Model." Electron. J. Probab. 15 1190 - 1266, 2010. https://doi.org/10.1214/EJP.v15-795

Information

Accepted: 9 August 2010; Published: 2010
First available in Project Euclid: 1 June 2016

zbMATH: 1226.60131
MathSciNet: MR2678390
Digital Object Identifier: 10.1214/EJP.v15-795

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

JOURNAL ARTICLE
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Vol.15 • 2010
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