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

被引：4

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

共 25 条

[1]

[Anonymous], 2002, P INT C MATHEMATICIA

[2]

Bakry Dominique, 1985, Seminaire de probabilites de Strasbourg, P177, DOI 10.1007/BFb0075847

[3]

BOBKOV S. G., 2022, ADV ANAL GEOM, V6, P135, DOI [10.1515/9783110741711-008, DOI 10.1515/9783110741711-008]

[4] WEIGHTED POINCARE-TYPE INEQUALITIES FOR CAUCHY AND OTHER CONVEX MEASURES [J].

Bobkov, Sergey G. ;

Ledoux, Michel .

ANNALS OF PROBABILITY, 2009, 37 (02) :403-427

[5] The log-Brunn-Minkowski inequality [J].

Boeroeczky, Karoly J. ;

Lutwak, Erwin ;

Yang, Deane ;

Zhang, Gaoyong .

ADVANCES IN MATHEMATICS, 2012, 231 (3-4) :1974-1997

[6]

Borell Bor75b Christer, 1975, Period.Math.Hungar, V6, P111

[7] CONVEX MEASURES ON LOCALLY CONVEX-SPACES [J].

BORELL, C .

ARKIV FOR MATEMATIK, 1974, 12 (02) :239-252

[8] ON EXTENSIONS OF BRUNN-MINKOWSKI AND PREKOPA-LEINDLER THEOREMS, INCLUDING INEQUALITIES FOR LOG CONCAVE FUNCTIONS, AND WITH AN APPLICATION TO DIFFUSION EQUATION [J].

BRASCAMP, HJ ;

LIEB, EH .

JOURNAL OF FUNCTIONAL ANALYSIS, 1976, 22 (04) :366-389

[9] From the Brunn-Minkowski inequality to a class of Poincare-type inequalities [J].

Colesanti, Andrea .

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2008, 10 (05) :765-772

[10] On the stability of Brunn-Minkowski type inequalities [J].

Colesanti, Andrea ;

Livshyts, Galyna V. ;

Marsiglietti, Arnaud .

JOURNAL OF FUNCTIONAL ANALYSIS, 2017, 273 (03) :1120-1139

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