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June, 1979 Renormalizing the 3-Dimensional Voter Model
Maury Bramson, David Griffeath
Ann. Probab. 7(3): 418-432 (June, 1979). DOI: 10.1214/aop/1176995043


It is shown that a discrete time voter model in equilibrium on $\mathbb{Z}_3$ approaches the 0-mass free field of 3-dimensional Euclidean field theory under appropriate renormalization. This result is of interest because the strong correlation between distant sites gives rise to the renormalization exponent $- \frac{5}{2}$ instead of the usual $- \frac{3}{2}.$ Dawson, Ivanoff, and Spitzer have examined models on $\mathbb{R}_3$ which exhibit precisely the same limit. Because the process we consider lives on a lattice, our method of proof is necessarily quite different from theirs. In particular, we make use of a "duality" between voter models and coalescing random walks which has been exploited effectively by Holley and Liggett.


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Maury Bramson. David Griffeath. "Renormalizing the 3-Dimensional Voter Model." Ann. Probab. 7 (3) 418 - 432, June, 1979.


Published: June, 1979
First available in Project Euclid: 19 April 2007

zbMATH: 0401.60107
MathSciNet: MR528320
Digital Object Identifier: 10.1214/aop/1176995043

Primary: 60K35

Keywords: Interacting particle system , renormalization , self-similar random field

Rights: Copyright © 1979 Institute of Mathematical Statistics


Vol.7 • No. 3 • June, 1979
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