Competing super-brownian motions as limits of interacting particle systems

Richard Durrett; Leonid Mytnik; Edwin Perkins

doi:10.1214/EJP.v10-229

Competing super-brownian motions as limits of interacting particle systems

Richard Durrett, Leonid Mytnik, Edwin Perkins

Data and Decision Sciences

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

Abstract

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.

Original language	English
Pages (from-to)	1147-1220
Number of pages	74
Journal	Electronic Journal of Probability
Volume	10
DOIs	https://doi.org/10.1214/EJP.v10-229
State	Published - 1 Jan 2005

Keywords

Collision local time
Competing species
Interacting branching particle system
Measure-valued diffusion
Super-Brownian motion

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

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10.1214/EJP.v10-229

Cite this

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AB - 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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KW - Competing species

KW - Interacting branching particle system

KW - Measure-valued diffusion

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Competing super-brownian motions as limits of interacting particle systems

Abstract

Keywords

ASJC Scopus subject areas

UN SDGs

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