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July 2001 Super-Brownian Limits of Voter Model Clusters
Maury Bramson, J.Theodore Cox, Jean-François Le Gall
Ann. Probab. 29(3): 1001-1032 (July 2001). DOI: 10.1214/aop/1015345593

Abstract

The voter model is one of the standard interacting particle systems. Two related problems for this process are to analyze its behavior, after large times $t$, for the sets of sites (1) sharing the same opinion as the site 0, and (2) having the opinion that was originally at 0. Results on the sizes of these sets were given by Sawyer (1979)and Bramson and Griffeath (1980). Here, we investigate the spatial structure of these sets in $d \geq 2$, which we show converge to quantities associated with super-Brownian motion, after suitable normalization. The main theorem from Cox, Durrett and Perkins (2000) serves as an important tool for these results.

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Maury Bramson. J.Theodore Cox. Jean-François Le Gall. "Super-Brownian Limits of Voter Model Clusters." Ann. Probab. 29 (3) 1001 - 1032, July 2001. https://doi.org/10.1214/aop/1015345593

Information

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

zbMATH: 1029.60078
MathSciNet: MR1872733
Digital Object Identifier: 10.1214/aop/1015345593

Subjects:
Primary: 60G57 , 60K35
Secondary: 60F05 , 60J80

Keywords: coalescing random walk , Super-Brownian motion , voter model

Rights: Copyright © 2001 Institute of Mathematical Statistics

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Vol.29 • No. 3 • July 2001
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