Rescaled voter models converge to super-Brownian motion.

DOI10.1214/aop/1019160117zbMath1044.60092OpenAlexW2011370313MaRDI QIDQ1872509

Edwin A. Perkins, J. Theodore Cox, Richard T. Durrett

Publication date: 6 May 2003

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.aop/1019160117

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Random measures (60G57) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

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Cites Work

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• Hydrodynamics of the voter model
• On the Skorokhod topology
• Stochastic partial differential equations for some measure-valued diffusions
• One dimensional stochastic partial differential equations and the branching measure diffusion
• Diffusive clustering in the two dimensional voter model
• Construction and regularity of measure-valued Markov branching processes
• Distribution function inequalities for martingales
• The carrying dimension of a stochastic measure diffusion
• Additive and cancellative interacting particle systems
• Rescaled contact processes converge to super-Brownian motion in two or more dimensions
• Statistical mechanics of crabgrass
• Super-Brownian limits of voter model clusters
• Stochastic p.d.e.'s arising from the long range contact and long range voter processes
• Hybrid zones and voter model interfaces
• A limit theorem of branching processes and continuous state branching processes
• Historical processes
• An Introduction to Branching Measure-Valued Processes
• Lattice trees and super-Brownian motion

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