TY - JOUR
T1 - Super-Brownian limits of voter model clusters
AU - Bramson, Maury
AU - Cox, J. Theodore
AU - Le Gall, Jean François
PY - 2001/7
Y1 - 2001/7
N2 - 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.
AB - 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.
KW - Coalescing random walk
KW - Super-Brownian motion
KW - Voter model
UR - http://www.scopus.com/inward/record.url?scp=0035562830&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0035562830&partnerID=8YFLogxK
U2 - 10.1214/aop/1015345593
DO - 10.1214/aop/1015345593
M3 - Article
AN - SCOPUS:0035562830
SN - 0091-1798
VL - 29
SP - 1001
EP - 1032
JO - Annals of Probability
JF - Annals of Probability
IS - 3
ER -