Variance asymptotics and central limit theorems for generalized growth processes with applications to convex hulls and maximal points

• 成果类型: Article
• 署名作者: Schreiber, T.; Yukich, J. E.
• 署名单位: Nicolaus Copernicus University; Lehigh University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117907000000259
• 发表日期: 2008
• 页码: 363-396
• 关键词: r-d; number

摘要

We show that the random point measures induced by vertices in the convex hull of a Poisson sample on the unit ball, when properly scaled and centered, converge to those of a mean zero Gaussian field. We establish limiting variance and covariance asymptotics in terms of the density of the Poisson sample. Similar results hold for the point measures induced by the maximal points in a Poisson sample. The approach involves introducing a generalized spatial birth growth process allowing for cell overlap.