FIXATION RESULTS FOR THRESHOLD VOTER SYSTEMS

被引：30

作者：

DURRETT, R ^{[1
]}

STEIF, JE ^{[1
]}

机构：

[1] GOTHENBURG UNIV,DEPT MATH & STAT,S-41124 GOTHENBURG,SWEDEN

来源：

ANNALS OF PROBABILITY | 1993年 / 21卷 / 01期

关键词：

CELLULAR AUTOMATA; LARGE DEVIATIONS; VOTER MODELS;

D O I：

10.1214/aop/1176989403

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

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.

引用

页码：232 / 247

页数：16

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