The Annals of Probability

Rescaled Lotka–Volterra models converge to super-Brownian motion

J. Theodore Cox and Edwin A. Perkins

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We show that a sequence of stochastic spatial Lotka–Volterra models, suitably rescaled in space and time, converges weakly to super-Brownian motion with drift. The result includes both long range and nearest neighbor models, the latter for dimensions three and above. These theorems are special cases of a general convergence theorem for perturbations of the voter model.

Article information

Ann. Probab., Volume 33, Number 3 (2005), 904-947.

First available in Project Euclid: 6 May 2005

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Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60G57: Random measures
Secondary: 60F17: Functional limit theorems; invariance principles 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)

Lotka–Volterra voter model super-Brownian motion spatial competition coalescing random walk


Cox, J. Theodore; Perkins, Edwin A. Rescaled Lotka–Volterra models converge to super-Brownian motion. Ann. Probab. 33 (2005), no. 3, 904--947. doi:10.1214/009117904000000973.

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