Super-Brownian limits of voter model clusters

Maury Bramson, J. Theodore Cox, Jean François Le Gall

Research output: Contribution to journalArticle

22 Scopus citations

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 languageEnglish (US)
Pages (from-to)1001-1032
Number of pages32
JournalAnnals of Probability
Volume29
Issue number3
StatePublished - Jul 1 2001

Keywords

  • Coalescing random walk
  • Super-Brownian motion
  • Voter model

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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    Bramson, M., Cox, J. T., & Le Gall, J. F. (2001). Super-Brownian limits of voter model clusters. Annals of Probability, 29(3), 1001-1032.