The complete convergence theorem for coexistent threshold voter models
成果类型：
Article
署名作者：
Handjani, SJ
署名单位：
University of Mississippi
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
发表日期：
1999
页码：
226-245
关键词：
摘要：
We consider the d-dimensional threshold voter model. It is known that, except in the one-dimensional nearest-neighbor case, coexistence occurs (nontrivial invariant measures exist). In fact, there is a nontrivial limit eta(infinity)(1/2) Obtained by starting from the product measure with density 1/2. We show that in these coexistent cases, eta(t) double right arrow alpha delta(0) + beta delta(1) (1- alpha - beta)eta(infinity)(1/2) as t --> infinity, where alpha = P(tau(0) < infinity), beta = P(tau(1) < infinity), tau(0) and tau(1) are the first hitting times of the all-zero and all-one configurations, respectively, and double right arrow denotes weak convergence.