Access the full text.
Sign up today, get DeepDyve free for 14 days.
S. Artstein-Avidan, D. Florentin, A. Segal (2017)
Polar Pr\'ekopa--Leindler InequalitiesarXiv: Functional Analysis
J. Melbourne (2018)
Rearrangements and information theoretic inequalities2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton)
L. Gross (1975)
LOGARITHMIC SOBOLEV INEQUALITIES.American Journal of Mathematics, 97
C. Shannon (1948)
A mathematical theory of communicationBell Syst. Tech. J., 27
M. Madiman, J. Melbourne, Peng Xu (2016)
Forward and Reverse Entropy Power Inequalities in Convex GeometryArXiv, abs/1604.04225
S. Bobkov, M. Ledoux (2009)
Weighted poincaré-type inequalities for cauchy and other convex measuresAnnals of Probability, 37
S. Bobkov, G. Chistyakov (2015)
Entropy Power Inequality for the Rényi EntropyIEEE Transactions on Information Theory, 61
N. Gozlan, C. Roberto, P. Samson, P. Tetali (2012)
Displacement convexity of entropy and related inequalities on graphsProbability Theory and Related Fields, 160
E. Carlen (1991)
Superadditivity of Fisher's information and logarithmic Sobolev inequalitiesJournal of Functional Analysis, 101
Arnaud Marsiglietti, J. Melbourne (2018)
A Renyi Entropy Power Inequality for Log-Concave Vectors and Parameters in [0, 1]2018 IEEE International Symposium on Information Theory (ISIT)
A. Rényi (1961)
On Measures of Entropy and Information
S. Bobkov, Arnaud Marsiglietti (2016)
Variants of the Entropy Power InequalityIEEE Transactions on Information Theory, 63
H. Brascamp, E. Lieb, J.M Luttinger (1974)
A general rearrangement inequality for multiple integralsJournal of Functional Analysis, 17
Jiange Li, Arnaud Marsiglietti, J. Melbourne (2016)
Rényi Entropy Power Inequalities for s-concave Densities2019 IEEE International Symposium on Information Theory (ISIT)
C. Shannon (1950)
The mathematical theory of communication
Jiange Li, Arnaud Marsiglietti, J. Melbourne (2019)
Entropic Central Limit Theorem for Rényi Entropy2019 IEEE International Symposium on Information Theory (ISIT)
Jiange Li, Arnaud Marsiglietti, J. Melbourne (2019)
Further Investigations of Rényi Entropy Power Inequalities and an Entropic Characterization of s-Concave DensitiesLecture Notes in Mathematics
A. Kechris (1987)
Classical descriptive set theory
W. Beckner (1975)
Inequalities in Fourier analysisAnnals of Mathematics, 102
Jiange Li, J. Melbourne (2018)
Further Investigations of the Maximum Entropy of the Sum of Two Dependent Random Variables2018 IEEE International Symposium on Information Theory (ISIT)
S. Bobkov, M. Ledoux (2000)
From Brunn-Minkowski to Brascamp-Lieb and to logarithmic Sobolev inequalitiesGeometric & Functional Analysis GAFA, 10
C. Borell (2007)
Inequalities of the Brunn–Minkowski type for Gaussian measuresProbability Theory and Related Fields, 140
A. Ehrhard (1983)
Symétrisation dans l'espace de Gauss.Mathematica Scandinavica, 53
F. Barthe, Nolwen Huet (2008)
On Gaussian Brunn-Minkowski inequalitiesarXiv: Probability
V. Sudakov, B. Tsirel'son (1978)
Extremal properties of half-spaces for spherically invariant measuresJournal of Soviet Mathematics, 9
Arnaud Marsiglietti, J. Melbourne (2017)
On the Entropy Power Inequality for the Rényi Entropy of Order [0, 1]IEEE Transactions on Information Theory, 65
A. Dembo, T. Cover, Joy Thomas (1991)
Information theoretic inequalitiesIEEE Trans. Inf. Theory, 37
Liyao Wang, M. Madiman (2013)
Beyond the Entropy Power Inequality, via RearrangementsIEEE Transactions on Information Theory, 60
N. Blachman (1965)
The convolution inequality for entropy powersIEEE Trans. Inf. Theory, 11
F. Barthe (1997)
On a reverse form of the Brascamp-Lieb inequalityInventiones mathematicae, 134
C. Borell (1975)
Convex set functions ind-spacePeriodica Mathematica Hungarica, 6
Eshed Ram, I. Sason (2016)
On Rényi entropy power inequalities2016 IEEE International Symposium on Information Theory (ISIT)
Joaquim Martín, M. Milman (2008)
Isoperimetry and symmetrization for logarithmic Sobolev inequalitiesJournal of Functional Analysis, 256
H. Brascamp, E. Lieb (1976)
On extensions of the Brunn-Minkowski and Prékopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equationJournal of Functional Analysis, 22
E. Lieb (1978)
Proof of an entropy conjecture of WehrlCommunications in Mathematical Physics, 62
M. Madiman, Liyao Wang, J. Woo (2017)
Majorization and Rényi entropy inequalities via Sperner theoryDiscret. Math., 342
S. Bobkov, I. Gentil, M. Ledoux (2001)
Hypercontractivity of Hamilton-Jacobi equationsJournal de Mathématiques Pures et Appliquées, 80
R. Zamir, M. Feder (1993)
A generalization of the entropy power inequality with applicationsIEEE Trans. Inf. Theory, 39
Joaquim Martín, M. Milman (2009)
Pointwise symmetrization inequalities for Sobolev functions and applicationsAdvances in Mathematics, 225
C. Borell (1974)
Convex measures on locally convex spacesArkiv för Matematik, 12
T. Cover, Joy Thomas (1991)
Elements of Information Theory
S. Artstein-Avidan, D. Florentin, A. Segal (2017)
Functional Brunn-Minkowski inequalities induced by polarityarXiv: Functional Analysis
Jiange Li (2017)
Rényi entropy power inequality and a reverseArXiv, abs/1704.02634
H. Brascamp, E. Lieb (1976)
Best Constants in Young's Inequality, Its Converse, and Its Generalization to More than Three FunctionsAdvances in Mathematics, 20
N. Gozlan, C. Roberto, P. Samson, P. Tetali (2019)
Transport Proofs of some discrete variants of the Prékopa-Leindler inequalityANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE
S. Bobkov, J. Melbourne (2014)
Hyperbolic measures on infinite dimensional spacesProbability Surveys, 13
C. Borell (1975)
The Brunn-Minkowski inequality in Gauss spaceInventiones mathematicae, 30
Y. Ollivier, C. Villani (2010)
A Curved Brunn-Minkowski Inequality on the Discrete Hypercube, Or: What Is the Ricci Curvature of the Discrete Hypercube?SIAM J. Discret. Math., 26
M. Costa, T. Cover (1984)
On the similarity of the entropy power inequality and the Brunn-Minkowski inequalityIEEE Trans. Inf. Theory, 30
M. Madiman, J. Melbourne, Peng Xu (2017)
Rogozin's convolution inequality for locally compact groupsarXiv: Probability
R. Starr (1969)
Quasi-Equilibria in Markets with Non-Convex PreferencesEconometrica, 37
A. Stam (1959)
Some Inequalities Satisfied by the Quantities of Information of Fisher and ShannonInf. Control., 2
[We investigate the interactions of functional rearrangements with Prékopa–Leindler type inequalities. It is shown that certain set theoretic rearrangement inequalities can be lifted to functional analogs, thus demonstrating that several important integral inequalities tighten on functional rearrangement about “isoperimetric” sets with respect to a relevant measure. Applications to the Borell–Brascamp–Lieb, Borell–Ehrhard, and the recent polar Prékopa–Leindler inequalities are demonstrated. It is also proven that an integrated form of the Gaussian log-Sobolev inequality sharpens on rearrangement.]
Published: Nov 27, 2019
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.