Renormalization of the two-dimensional Lotka-Volterra model

J. Theodore Cox; Edwin A. Perkins

doi:10.1214/07-AAP453

Renormalization of the two-dimensional Lotka-Volterra model

J. Theodore Cox, Edwin A. Perkins

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

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.

Original language	English (US)
Pages (from-to)	747-812
Number of pages	66
Journal	Annals of Applied Probability
Volume	18
Issue number	2
DOIs	https://doi.org/10.1214/07-AAP453
State	Published - Apr 2008

Keywords

Lotka-Volterra model
Super-brownian motion
Voter model

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/07-AAP453

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title = "Renormalization of the two-dimensional Lotka-Volterra model",

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.",

keywords = "Lotka-Volterra model, Super-brownian motion, Voter model",

author = "Cox, {J. Theodore} and Perkins, {Edwin A.}",

year = "2008",

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AB - 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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KW - Super-brownian motion

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Renormalization of the two-dimensional Lotka-Volterra model

Abstract

Keywords

ASJC Scopus subject areas

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