Random approximation and the vertex index of convex bodies

被引：4

作者：

Brazitikos, Silouanos ^{[1
]}

Chasapis, Giorgos ^{[1
]}

Hioni, Labrini ^{[1
]}

机构：

[1] Natl & Kapodistrian Univ Athens, Dept Math, Athens 15784, Greece

来源：

ARCHIV DER MATHEMATIK | 2017年 / 108卷 / 02期

关键词：

Convex bodies; Isotropic position; Centroid bodies; Random polytopal approximation;

D O I：

10.1007/s00013-016-0975-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that there exists an absolute constant with the following property: if K is a convex body in whose center of mass is at the origin, then a random subset of cardinality satisfies with probability greater than K subset of c(2)n conv(X) where are absolute constants. As an application we show that the vertex index of any convex body K in is bounded by , where is an absolute constant, thus extending an estimate of Bezdek and Litvak for the symmetric case.

引用

页码：209 / 221

页数：13

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