A LARGE-DIMENSIONAL INDEPENDENT AND IDENTICALLY DISTRIBUTED PROPERTY FOR NEAREST NEIGHBOR COUNTS IN POISSON PROCESSES
成果类型：
Article
署名作者：
Yao, Yi-Ching; Simons, Gordon
署名单位：
Colorado State University System; Colorado State University Fort Collins; Academia Sinica - Taiwan; University of North Carolina; University of North Carolina Chapel Hill
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
发表日期：
1996
页码：
561-571
关键词：
摘要：
For an arbitrary point of a homogeneous Poisson point process in a d-dimensional Euclidean space, consider the number of Poisson points that have that given point as their rth nearest neighbor (r = 1, 2, ...). It is shown that as d tends to infinity, these nearest neighbor counts (r = 1, 2, ...) are iid asymptotically Poisson with mean 1. The proof relies on Renyi's characterization of Poisson processes and a representation in the limit of each nearest neighbor count as a sum of countably many dependent Bernoulli random variables.