Modified Brascamp-Lieb inequalities and log-Sobolev inequalities for one-dimensional log-concave measure

被引：0

作者：

Wu, Denghui ^{[1
]}

Zhou, Jiazu ^{[2
]}

机构：

[1] Northwest A&F Univ, Coll Sci, Yangling 712100, Peoples R China

[2] Guizhou Educ Univ, Sch Math & Big Data, Guiyang 550018, Peoples R China

来源：

ACTA MATHEMATICA SCIENTIA | 2025年 / 45卷 / 01期

关键词：

Brunn-Minkowski inequality; Pr & eacute; kopa-Leindler inequality; Brascamp-Lieb inequality; log-Sobolev inequality; log-concave measure; BRUNN-MINKOWSKI; LOGARITHMIC SOBOLEV; STABILITY;

D O I：

10.1007/s10473-025-0108-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we develop Maurey's and Bobkov-Ledoux's methods to prove modified Brascamp-Lieb inequalities and log-Sobolev inequalities for one-dimensional log-concave measure. To prove these inequalities, the harmonic Pr & eacute;kopa-Leindler inequality is used. We prove that these new inequalities are more efficient in estimating the variance and entropy for some functions with exponential terms.

引用

页码：104 / 117

页数：14

共 27 条

[11] A characterization of a class of convex log-Sobolev inequalities on the real line [J].

Shu, Yan ;

Strzelecki, Michal .

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2018, 54 (04) :2075-2091

[12] Dimension-free log-Sobolev inequalities for mixture distributions [J].

Chen, Hong-Bin ;

Chewi, Sinho ;

Niles-Weed, Jonathan .

JOURNAL OF FUNCTIONAL ANALYSIS, 2021, 281 (11)

[13] Log-Sobolev and Nash Inequalities for Discrete-Time Finite Markov Chains [J].

Song, Yan-Hong .

MARKOV PROCESSES AND RELATED FIELDS, 2015, 21 (01) :127-144

[14] Sharp log-Sobolev inequalities in CD(0, N) spaces with applications [J].

Balogh, Zoltan M. ;

Kristaly, Alexandru ;

Tripaldi, Francesca .

JOURNAL OF FUNCTIONAL ANALYSIS, 2024, 286 (02)

[15] A simple proof of log-Sobolev inequalities on a path space with Gibbs measures [J].

Kawabi, H .

INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS, 2006, 9 (02) :321-329

[16] Time-uniform log-Sobolev inequalities and applications to propagation of chaos [J].

Monmarche, Pierre ;

Ren, Zhenjie ;

Wang, Songbo .

ELECTRONIC JOURNAL OF PROBABILITY, 2024, 29

[17] Dimensional variance inequalities of Brascamp-Lieb type and a local approach to dimensional Prekopa's theorem [J].

Van Hoang Nguyen .

JOURNAL OF FUNCTIONAL ANALYSIS, 2014, 266 (02) :931-955

[18] Riemannian metrics on convex sets with applications to Poincare and log-Sobolev inequalities [J].

Kolesnikov, Alexander V. ;

Milman, Emanuel .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2016, 55 (04)

[19] CONCENTRATION INEQUALITIES FOR LOG-CONCAVE DISTRIBUTIONS WITH APPLICATIONS TO RANDOM SURFACE FLUCTUATIONS [J].

Magazinov, Alexander ;

Peled, Ron .

ANNALS OF PROBABILITY, 2022, 50 (02) :735-770

[20] The first variation of the total mass of log-concave functions and related inequalities [J].

Colesanti, Andrea ;

Fragala, Ilaria .

ADVANCES IN MATHEMATICS, 2013, 244 :708-749

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