The Annals of Applied Probability

Renormalization of the two-dimensional Lotka–Volterra model

J. Theodore Cox and Edwin A. Perkins

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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.

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Ann. Appl. Probab., Volume 18, Number 2 (2008), 747-812.

First available in Project Euclid: 20 March 2008

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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.)

Voter model super-Brownian motion Lotka–Volterra model


Cox, J. Theodore; Perkins, Edwin A. Renormalization of the two-dimensional Lotka–Volterra model. Ann. Appl. Probab. 18 (2008), no. 2, 747--812. doi:10.1214/07-AAP453.

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