A strong law for the longest edge of the minimal spanning tree

• 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
• 发表日期: 1999
• 页码: 246-260
• 关键词: points

摘要

Suppose X-1, X-2, X-3,... are independent random points in R-d, d greater than or equal to 2, with common density f, having connected compact support Omega with smooth boundary partial derivative Omega, with f/Omega continuous. Let M-n denote the smallest r such that the union of balls of diameter r centered at the first n points is connected. Let theta denote the volume of the unit ball. Then as n --> infinity, [GRAPHICS]