Gaussian limits for random measures in geometric probability

• 成果类型: Article
• 署名作者: Baryshnikov, Y; Yukich, JE
• 署名单位: AT&T; Alcatel-Lucent; Lucent Technologies; Lehigh University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051604000000594
• 发表日期: 2005
• 页码: 213-253
• 关键词: packing; MODEL

摘要

We establish Gaussian limits for general measures induced by binomial and Poisson point processes in d-dimensional space. The limiting Gaussian field has a covariance functional which depends on the density of the point process. The general results are used to deduce central limit theorems for measures induced by random graphs (nearest neighbor, Voronoi and sphere of influence graph), random sequential packing models (ballistic deposition and spatial birth-growth models) and statistics of germ-grain models.