Reverse Brunn-Minkowski and reverse entropy power inequalities for convex measures
From MaRDI portal
Publication:408149
DOI10.1016/j.jfa.2012.01.011zbMath1246.52012arXiv1109.5287OpenAlexW2133318567MaRDI QIDQ408149
Mokshay Madiman, Sergey G. Bobkov
Publication date: 29 March 2012
Published in: Journal of Functional Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1109.5287
Brunn-Minkowski inequalityconvex measureentropy estimateslog-concave probability distributionsvolume estimates
Inequalities; stochastic orderings (60E15) Length, area, volume and convex sets (aspects of convex geometry) (52A38)
Related Items
Entropy and set cardinality inequalities for partition-determined functions, On the sine polarity and the \(L_p\)-sine Blaschke-Santaló inequality, John's ellipsoid and the integral ratio of a log-concave function, Thin-shell concentration for convex measures, Functional covering numbers, On the equivalence of statistical distances for isotropic convex measures, Concentration of information content for convex measures, Weighted Brunn-Minkowski theory. I: On weighted surface area measures, On the analogue of the concavity of entropy power in the Brunn-Minkowski theory, Stability of Cramer’s Characterization of Normal Laws in Information Distances, Optimal Concentration of Information Content for Log-Concave Densities, Some remarks on petty projection of log-concave functions, Volumes of subset Minkowski sums and the Lyusternik region, A discrete complement of Lyapunov's inequality and its information theoretic consequences, Dimensional behaviour of entropy and information, On the volume of the Minkowski sum of zonoids, Further Investigations of Rényi Entropy Power Inequalities and an Entropic Characterization of s-Concave Densities, Bernoulli sums and Rényi entropy inequalities, Convex geometry and its applications. Abstracts from the workshop held December 12--18, 2021 (hybrid meeting), On isoperimetric inequality in Arakelov geometry, Rényi entropy power inequality and a reverse, Hodge index inequality in geometry and arithmetic: a probabilistic approach, The convexification effect of Minkowski summation, Bounds on the maximum of the density for sums of independent random variables, Unnamed Item, A note on volume thresholds for random polytopes, A Combinatorial Approach to Small Ball Inequalities for Sums and Differences, A reverse entropy power inequality for log-concave random vectors, On the Problem of Reversibility of the Entropy Power Inequality
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A Mathematical Theory of Communication
- Dimensional behaviour of entropy and information
- Concentration of the information in data with log-concave distributions
- A Freĭman-type theorem for locally compact Abelian groups
- Brunn-Minkowskischer Satz und Isoperimetrie
- The difference body of a convex body
- Increasing functions and inverse Santaló inequality for unconditional functions
- Convex measures on locally convex spaces
- On extensions of the Brunn-Minkowski and Prekopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation
- Sections of convex bodies through their centroid
- Entropy and asymptotic geometry of non-symmetric convex bodies
- Volumes of restricted Minkowski sums and the free analogue of the entropy power inequality
- Convex set functions in \(d\)-space
- Product set estimates for non-commutative groups
- Convex bodies and norms associated to convex measures
- The M-ellipsoid, symplectic capacities and volume
- A central limit theorem for convex sets
- Large deviations and isoperimetry over convex probability measures with heavy tails
- Complements of Lyapunov's inequality
- Geometry of log-concave functions and measures
- Verallgemeinerung eines Mittelwertsatzes von J. Favard für positive konkave Funktionen
- On the Problem of Reversibility of the Entropy Power Inequality
- Geometric inequalities for a class of exponential measures
- On the similarity of the entropy power inequality and the Brunn- Minkowski inequality (Corresp.)
- Convex Bodies Associated with a Given Convex Body
- Some inequalities satisfied by the quantities of information of Fisher and Shannon
- Generalized Entropy Power Inequalities and Monotonicity Properties of Information
- Plünnecke’s Inequality for Different Summands
- A new entropy power inequality
- Logarithmically concave functions and sections of convex sets in $R^{n}$
- Information theoretic inequalities
- A short proof of the "concavity of entropy power"
- Solution of Shannon’s problem on the monotonicity of entropy
- The Entropy Per Coordinate of a Random Vector is Highly Constrained Under Convexity Conditions
- Eine zahlentheoretische Anwendung der Graphentheorie.