ASYMPTOTIC NORMALITY FOR RANDOM SIMPLICES AND CONVEX BODIES IN HIGH DIMENSIONS

被引：6

作者：

Alonso-Gutierrez, D. ^{[1
]}

Besau, F. ^{[2
]}

Grote, J. ^{[3
]}

Kabluchko, Z. ^{[4
]}

Reitzner, M. ^{[5
]}

Thale, C. ^{[6
]}

Vritsiou, B-H ^{[7
]}

Werner, E. ^{[8
]}

机构：

[1] Univ Zaragoza, Dept Math, Pedro Cerbuna 12, Zaragoza, Spain

[2] Vienna Univ Technol, Fac Math, Oskar Morgenstern Pl, A-1090 Vienna, Austria

[3] Univ Ulm, Fac Math & Econ, D-89069 Ulm, Germany

[4] Univ Munster, Fac Math & Comp Sci, Einstein Str 62, D-48149 Munster, Germany

[5] Univ Osnabruck, Sch Math Comp Sci, Albrechtstr 28A, D-49069 Osnabruck, Germany

[6] Ruhr Univ Bochum, Dept Math, Univ Str 150, D-44801 Bohum, Germany

[7] Univ Alberta Edmonton, Dept Math, Edmonton, AB T6G 2G1, Canada

[8] Case Western Reserve Univ, Dept Math Appl Math & Stat, Yost Hall,2049 Martin Luther King Jr Dr, Cleveland, OH 44106 USA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2021年 / 149卷 / 01期

关键词：

Central limit theorem; high dimensions; l(p)-ball; random convex body; random determinant; random parallelotope; random polytope; random simplex; stochastic geometry; VOLUME; BALL;

D O I：

10.1090/proc/15232

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Central limit theorems for the log-volume of a class of random convex bodies in R-n are obtained in the high-dimensional regime, that is, as n -> infinity. In particular, the case of random simplices pinned at the origin and simplices where all vertices are generated at random is investigated. The coordinates of the generating vectors are assumed to be independent and identically distributed with subexponential tails. In addition, asymptotic normality is also established for random convex bodies (including random simplices pinned at the origin) when the spanning vectors are distributed according to a radially (s)ymmetric probability measure on the n-dimensional l(p)-ball. In particular, this includes the cone and the uniform probability measure.

引用

页码：355 / 367

页数：13

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