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July 2001 Renormalization of the Voter Model in Equilibrium
Iljana Zähle
Ann. Probab. 29(3): 1262-1302 (July 2001). DOI: 10.1214/aop/1015345603


We consider the $d$-dimensional voter model for $d \geq 3$. Our interest is the large scale limit of the equilibrium state of the voter model, where we prove the $d = 3$ results of [1] for $d \geq 4$, which turn out to be of a different nature than for $d = 3$. For this purpose we use the historical process.We establish some surprising facts about the Green’s function of random walks in dimension $d \geq 4$,which lead to the different features in $d = 3$ versus $d \geq 4$. Secondly, we prove an analogous result for the voter model on the hierarchical group.


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Iljana Zähle. "Renormalization of the Voter Model in Equilibrium." Ann. Probab. 29 (3) 1262 - 1302, July 2001.


Published: July 2001
First available in Project Euclid: 5 March 2002

zbMATH: 1023.60081
MathSciNet: MR1872743
Digital Object Identifier: 10.1214/aop/1015345603

Primary: 60K35

Keywords: Green's function of random walks , interacting particle systems , renormalization

Rights: Copyright © 2001 Institute of Mathematical Statistics


Vol.29 • No. 3 • July 2001
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