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2005 Competing super-Brownian motions as limits of interacting particle systems
Richard Durrett, Leonid Mytnik, Edwin Perkins
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Electron. J. Probab. 10: 1147-1220 (2005). DOI: 10.1214/EJP.v10-229


We study two-type branching random walks in which the birth or death rate of each type can depend on the number of neighbors of the opposite type. This competing species model contains variants of Durrett's predator-prey model and Durrett and Levin's colicin model as special cases. We verify in some cases convergence of scaling limits of these models to a pair of super-Brownian motions interacting through their collision local times, constructed by Evans and Perkins.


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Richard Durrett. Leonid Mytnik. Edwin Perkins. "Competing super-Brownian motions as limits of interacting particle systems." Electron. J. Probab. 10 1147 - 1220, 2005.


Accepted: 9 September 2005; Published: 2005
First available in Project Euclid: 1 June 2016

zbMATH: 1111.60030
MathSciNet: MR2164042
Digital Object Identifier: 10.1214/EJP.v10-229

Primary: 60G57
Secondary: 60G17

Keywords: Collision local time , Competing species , interacting branching particle systems , measure-valued diffusions , Super-Brownian motion

Vol.10 • 2005
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