THE RSW THEOREM FOR CONTINUUM PERCOLATION AND THE CLT FOR EUCLIDEAN MINIMAL SPANNING TREES
成果类型：
Article
署名作者：
Alexander, Kenneth S.
署名单位：
University of Southern California
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
发表日期：
1996
页码：
466-494
关键词：
摘要：
We prove a central limit theorem for the length of the minimal spanning tree of the set of sites of a Poisson process of intensity lambda in [0, 1](2) as lambda -> infinity. As observed previously by Ramey, the main difficulty is the dependency between the contributions to this length from different regions of [0, 1](2); a percolation-theoretic result on circuits surrounding a fixed site can be used to control this dependency. We prove such a result via a continuum percolation version of the Russo-Seymour-Welsh theorem for occupied crossings of a rectangle. This RSW theorem also yields a variety of results for two-dimensional fixed-radius continuum percolation already well known for lattice models, including a finite-box criterion for percolation and absence of percolation at the critical point.