THE THRESHOLD VOTER AUTOMATON AT A CRITICAL-POINT
成果类型：
Article
署名作者：
STEIF, JE
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1176988597
发表日期：
1994
页码：
1121-1139
关键词：
摘要：
We consider the threshold voter automaton in one dimension with threshold tau > n/2, where n is the number of neighbors and where we start from a product measure with density 1/2. It has recently been shown that there is a critical value theta(c) approximate to 0.6469076, so that if tau = theta n with theta > theta(c) and n is large, then most sites never flip, while for theta epsilon (1/2, theta(c)) and n large, there is a limiting state consisting mostly of large regions of points of the same type. Using a supercritical branching process, we show that the behavior at theta(c) differs from both the theta > theta(c) regime and the theta < theta(c) regime and that, in some sense, there is a discontinuity both from the left and from the right at this critical value.