FINITE AND INFINITE SYSTEMS OF INTERACTING DIFFUSIONS

• 成果类型: Article
• 署名作者: COX, JT; GREVEN, A; SHIGA, T
• 署名单位: University of Erlangen Nuremberg; Institute of Science Tokyo; Tokyo Institute of Technology
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/BF01204213
• 发表日期: 1995
• 页码: 165-197
• 关键词: ergodic-theorems; random-walks; voter model; times

摘要

We study the problem of relating the long time behavior of finite and infinite systems of locally interacting components. We consider in detail a class of linearly interacting diffusions x(t) = {x(i)(t), i is an element of Z(d)}, in the regime where there is a one-parameter family of nontrivial invariant measures. For these systems there are naturally defined corresponding finite systems, x(N)(t) = {x(i)(N)(t), i is an element of Lambda(N)}, with Lambda(N) = (-N,N](d) boolean AND Z(d). Our main result gives a comparison between the laws of x(t(N)) and x(N)(t(N)) for times t(N) --> infinity as N --> infinity. The comparison involves certain mixtures of the invariant measures for the infinite system.