Super-Brownian limits of voter model clusters

• 成果类型: Article
• 署名作者: Bramson, M; Cox, JT; Le Gall, JF
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities; Syracuse University; Universite PSL; Ecole Normale Superieure (ENS)
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2001
• 页码: 1001-1032
• 关键词: motion

摘要

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 greater than or equal to 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.