voter model cluster, Super-Brownian limits, interacting particle systems
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 (a) sharing the same opinion as the site 0, and (b) having the opinion that was originally at 0. Results on the sizes of these sets were given in [Sa79] and [BG80]. Here, we investigate the spatial structure of these sets in d ≥ 2, which we show converge to quantities associated with super-Brownian motion, after suitable normalization. The main theorem from [CDP98] serves as an important tool for these results.
Bramzon, Maury; Cox, J. Theodore; and Le Gall, Jean-Francois, "Super-Brownian Limits of Voter Model Clusters" (2000). Mathematics Faculty Scholarship. Paper 5.
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