Central limit theorems for random polytopes

被引：54

作者：

Reitzner, M ^{[1
]}

机构：

[1] Univ Technol Vienna, Inst Discrete Math & Geometry, A-1040 Vienna, Austria

来源：

PROBABILITY THEORY AND RELATED FIELDS | 2005年 / 133卷 / 04期

关键词：

random polytopes; CLT; approximation of convex bodies; dependency graph;

D O I：

10.1007/s00440-005-0441-8

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Let K be a smooth convex set. The convex hull of independent random points in K is a random polytope. Central limit theorems for the volume and the number of i dimensional faces of random polytopes are proved as the number of random points tends to infinity. One essential step is to determine the precise asymptotic order of the occurring variances.

引用

页码：483 / 507

页数：25

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