FIXATION RESULTS FOR THRESHOLD VOTER SYSTEMS
成果类型：
Article
署名作者：
DURRETT, R; STEIF, JE
署名单位：
University of Gothenburg
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1176989403
发表日期：
1993
页码：
232-247
关键词：
摘要：
We consider threshold voter systems in which the threshold tau > n/2, where n is the number of neighbors, and we present results in support of the following picture of what happens starting from product measure with density 1/2. The system fixates, that is, each site flips only finitely many times. There is a critical value, theta(c), so that if tau = thetan with theta > theta(c) and n is large then most sites never flip, while for theta is-an-element-of (1/2, theta(c)) and n large, the limiting state consists mostly of large regions of points of the same type. In d = 1, theta(c) almost-equal-to 0.6469076 while in d > 1, theta(c) = 3/4.