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 ≥ 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.
Original language | English (US) |
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Pages (from-to) | 1001-1032 |
Number of pages | 32 |
Journal | Annals of Probability |
Volume | 29 |
Issue number | 3 |
DOIs | |
State | Published - Jul 2001 |
Keywords
- Coalescing random walk
- Super-Brownian motion
- Voter model
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty