Document Type

Article

Date

2000

Embargo Period

10-2011

Keywords

voter model cluster, Super-Brownian limits, interacting particle systems

Language

English

Disciplines

Mathematics

Description/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 (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.

Creative Commons License

Creative Commons Attribution 3.0 License
This work is licensed under a Creative Commons Attribution 3.0 License.

Included in

Mathematics Commons

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