ON THE ASYMPTOTIC DISTRIBUTION OF THE AREA OUTSIDE A RANDOM CONVEX HULL IN A DISK
成果类型：
Article
署名作者：
Hsing, Tailen
署名单位：
Texas A&M University System; Texas A&M University College Station
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/aoap/1177005069
发表日期：
1994
页码：
478-493
关键词：
摘要：
The asymptotic distribution of the area V-n outside the convex hull of n i.i.d. points uniformly distributed on the two-dimensional unit disk is studied. The asymptotic variance of V-n is found to be of the order n(-5/3), and the asymptotic distribution of V-n shown to be normal. The results are obtained by carefully analyzing the strength of dependence between sample points at different locations close to the boundary of the unit disk.