Weighted Poincaré-type inequalities for Cauchy and other convex measures
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Publication:1019083
DOI10.1214/08-AOP407zbMath1178.46041arXiv0906.1651MaRDI QIDQ1019083
Sergey G. Bobkov, Michel Ledoux
Publication date: 27 May 2009
Published in: The Annals of Probability (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0906.1651
logarithmic Sobolev inequalitiesmeasure concentrationBrascamp-Lieb-type inequalityCheeger-type inequalitiesinfimum convolutionweighted Poincaré-type inequalities
General theory of stochastic processes (60G07) Measures and integration on abstract linear spaces (46G12) Probability theory on linear topological spaces (60B11)
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Cites Work
- Unnamed Item
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- Hardy-Poincaré inequalities and applications to nonlinear diffusions
- Asymptotics of the fast diffusion equation via entropy estimates
- Analytic inequalities, isoperimetric inequalities and logarithmic Sobolev inequalities
- Brunn-Minkowski inequality and its aftermath
- Some deviation inequalities
- Convex measures on locally convex spaces
- Convex set functions in d-space
- On extensions of the Brunn-Minkowski and Prekopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation
- Isoperimetric and analytic inequalities for log-concave probability measures
- From Brunn-Minkowski to Brascamp-Lieb and to logarithmic Sobolev inequalities
- Hypercontractivity of Hamilton-Jacobi equations.
- Fast diffusion to self-similarity: Complete spectrum, long-time asymptotics, and numerology
- Isoperimetric problems for convex bodies and a localization lemma
- Moment estimates derived from Poincaré and logarithmic Sobolev inequalities
- Large deviations and isoperimetry over convex probability measures with heavy tails
- A Topological Application of the Isoperimetric Inequality
- A Geometric Approach to Maximum Likelihood Estimation for Infinite- Dimensional Gaussian Location. II
- Random walks in a convex body and an improved volume algorithm
- The Brunn-Minkowski inequality
- Hardy's inequality with weights