Annals of Probability

Super-Brownian Limits of Voter Model Clusters

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.

Article information

Source
Ann. Probab., Volume 29, Number 3 (2001), 1001-1032.

Dates
First available in Project Euclid: 5 March 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1015345593

Digital Object Identifier
doi:10.1214/aop/1015345593

Mathematical Reviews number (MathSciNet)
MR1872733

Zentralblatt MATH identifier
1029.60078

Citation

Bramson, Maury; Cox, J.Theodore; Le Gall, Jean-François. Super-Brownian Limits of Voter Model Clusters. Ann. Probab. 29 (2001), no. 3, 1001--1032. doi:10.1214/aop/1015345593. https://projecteuclid.org/euclid.aop/1015345593

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