Maximal Surface Area of a Convex Set in Rn with Respect to Log Concave Rotation Invariant Measures

被引：12

作者：

Livshyts, Galyna ^{[1
]}

机构：

[1] Kent State Univ, Dept Math Sci, Kent, OH 44242 USA

来源：

GEOMETRIC ASPECTS OF FUNCTIONAL ANALYSIS: ISRAEL SEMINAR (GAFA) 2011-2013 | 2014年 / 2116卷

基金：

美国国家科学基金会;

关键词：

CENTRAL-LIMIT-THEOREM;

D O I：

10.1007/978-3-319-09477-9_23

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It was shown by K. Ball and F. Nazarov, that the maximal surface area of a convex set in R-n with respect to the Standard Gaussian measure is of order n(1/4). In the present paper we establish the analogous result for all rotation invariant log concave probability measures. We show that the maximal surface area with respect to such measures is of order root n/(4)root var vertical bar X vertical bar root E vertical bar X, where X is a random vector in R-n distributed with respect to the measure.

引用

页码：355 / 383

页数：29

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