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

共 50 条

[21] Gaussian polytopes: Variances and limit theorems
Hug, D
Reitzner, M
ADVANCES IN APPLIED PROBABILITY, 2005, 37 (02) : 297 - 320
[22] Central limit theorems for Gaussian polytopes (vol 35, pg 1593, 2007)
Barany, Imre
Vu, Van
ANNALS OF PROBABILITY, 2008, 36 (05): : 1998 - 1998
[23] Central limit theorems for iterated random Lipschitz mappings
Hennion, H
Hervé, L
ANNALS OF PROBABILITY, 2004, 32 (3A): : 1934 - 1984
[24] CENTRAL LIMIT THEOREMS CONDITIONALLY LINEAR RANDOM PROCESSES
PIERRE, PA
SIAM JOURNAL ON APPLIED MATHEMATICS, 1971, 20 (03) : 449 - +
[25] Central limit theorems for random permanents with correlation structure
Rempala, GA
Wesolowski, J
JOURNAL OF THEORETICAL PROBABILITY, 2002, 15 (01) : 63 - 76
[26] Empirical central limit theorems for exchangeable random variables
Jiang, XX
Hahn, MG
STATISTICS & PROBABILITY LETTERS, 2002, 59 (01) : 75 - 81
[27] Almost sure central limit theorems for random functions
Chuanrong Lu
Jin Qiu
Jianjun Xu
Science in China Series A: Mathematics, 2006, 49 : 1788 - 1799
[28] Multivariate central limit theorems for random clique complexes
Temčinas T.
Nanda V.
Reinert G.
Journal of Applied and Computational Topology, 2024, 8 (6) : 1837 - 1880
[29] RANDOM POLYNOMIALS: CENTRAL LIMIT THEOREMS FOR THE REAL ROOTS
Nguyen, Oanh
Van vu
DUKE MATHEMATICAL JOURNAL, 2021, 170 (17) : 3745 - 3813
[30] Central Limit Theorems for Uniform Model Random Polygons
John Pardon
Journal of Theoretical Probability, 2012, 25 : 823 - 833

← 1 2 3 4 5 →