IMPROVED LOG-CONCAVITY FOR ROTATIONALLY INVARIANT MEASURES OF SYMMETRIC CONVEX SETS

被引：3

作者：

Cordero-Erausquin, Dario ^{[1
]}

Rotem, Liran ^{[2
]}

机构：

[1] Sorbonne Univ, Inst Math Jussieu, Paris, France

[2] Technion Israel Inst Technol, Fac Math, Haifa, Israel

来源：

ANNALS OF PROBABILITY | 2023年 / 51卷 / 03期

关键词：

(B) conjecture; Gardner-Zvavitch conjecture; log-concavity; Brunn-Minkowski; Brascamp-Lieb inequality; Poincare inequality; BRUNN-MINKOWSKI INEQUALITIES; SMALL BALL PROBABILITY; POINCARE;

D O I：

10.1214/22-AOP1604

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：

We prove that the (B) conjecture and the Gardner-Zvavitch conjecture are true for all log-concave measures that are rotationally invariant, extend-ing previous results known for Gaussian measures. Actually, our result apply beyond the case of log-concave measures, for instance, to Cauchy measures as well. For the proof, new sharp weighted Poincare inequalities are obtained for even probability measures that are log-concave with respect to a rotation-ally invariant measure.

引用

页码：987 / 1003

页数：17

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