SURVIVAL OF DISCRETE TIME GROWTH MODELS, WITH APPLICATIONS TO ORIENTED PERCOLATION
成果类型：
Article
署名作者：
Liggett, Thomas M.
署名单位：
University of California System; University of California Los Angeles
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/aoap/1177004698
发表日期：
1995
页码：
613-636
关键词：
摘要：
We prove survival for a class of discrete time Markov processes whose states are finite sets of integers. As applications, we obtain upper bounds for the critical values of various two-dimensional oriented percolation models. The technique of proof is based generally on that used by Holley and Liggett to prove survival of the one-dimensional basic contact process. However, the fact that our processes evolve in discrete time requires that we make substantial changes in the way this technique is used. When applied to oriented percolation on the two-dimensional square lattice, our result gives the following bounds: p(c) <= 2/3 for bond percolation and p(c) <= 3/4 for site percolation.