A central limit theorem with applications to percolation, epidemics and Boolean models

• 成果类型: Article
• 署名作者: Penrose, MD
• 署名单位: Durham University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1015345760
• 发表日期: 2001
• 页码: 1515-1546
• 关键词: large deviations

摘要

Suppose X = (X-x)(xis an element ofZ)(d) is a white noise process, and H(B), defined for finite subsets B of Z(d), is determined in a stationary way by the restriction of X to B. Using a martingale approach, we prove a central limit theorem (CLT) for H as B becomes large, subject to H satisfying a stabilization condition (the effect of changing X-x at a single site needs to be local). This CLT is then applied to component counts for percolation and Boolean models, to the size of the big cluster for percolation on a box, and to the final size of a spatial epidemic.