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The entropy power inequality, which plays a fundamental role in information theory and probability, may be seen as an analogue of the Brunn-Minkowski inequality.
On the multiplication of successions of Fourier constants
W. H. Young · 1912
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Uber affine Geometrie VII: Neue Extremeingenschaften von Ellipse und Ellipsoid
W. Blaschke · 1917
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Die Brunn-Minkowskische ungleichung fur beliebige messbare mengen
L. A. Lusternik · 1935
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A mathematical theory of communication
C.E. Shannon · 1948
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A theorem on convex bodies of the Brunn-Minkowski type
H. Busemann · 1949
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An affine invariant for convex bodies of n n -dimensional space
L. A. Santaló · 1949
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The difference body of a convex body
C. A. Rogers and G. C. Shephard · 1957
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Some inequalities satisfied by the quantities of information of Fisher and Shannon
A.J. Stam · 1959
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The convolution inequality for entropy powers
N.M. Blachman · 1965
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Asymptotic behavior of products C p = C + ⋯ + C C^{p}=C+\cdots+C in locally compact abelian groups
W. R. Emerson and F. P. Greenleaf · 1969
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Quasi-equilibria in markets with non-convex preferences
R. M. Starr · 1969
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Convex Analysis
R.T. Rockafellar · 1970
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Logarithmic concave measures with application to stochastic programming
A. Prékopa · 1971
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On a certain converse of Hölder’s inequality
L. Leindler · 1972
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On a certain converse of Hölder’s inequality. II
L. Leindler · 1972
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Stability of the solution of a Minkowski equation
V. I. Diskant · 1973
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On logarithmic concave measures and functions
A. Prékopa · 1973
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Convex measures on locally convex spaces
C. Borell · 1974
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Inequalities in Fourier analysis
W. Beckner · 1975
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Convex set functions in d d -space
C. Borell · 1975
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Best constants in Young’s inequality, its converse, and its generalization to more than three functions
H. J. Brascamp and E. H. Lieb · 1976
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On extensions of the Brunn-Minkowski and Prékopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation
H. J. Brascamp and E. H. Lieb · 1976
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Proof of an entropy conjecture of Wehrl
E. H. Lieb · 1978
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Slicing convex bodies—bounds for slice area in terms of the body’s covariance
D. Hensley · 1980
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On the similarity of the entropy power inequality and the Brunn-Minkowski inequality
M.H.M. Costa and T.M. Cover · 1984
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Diffusions hypercontractives
D. Bakry and M. Émery · 1985
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A new entropy power inequality
M.H.M. Costa · 1985
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Affine isoperimetric problems
C. M. Petty · 1985
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Cube slicing in 𝐑 n {\bf R}^{n}
K. Ball · 1986
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Isometric problems in ℓ p \ell^{p} and sections of convex sets
K. Ball · 1986
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Inégalité de Brunn-Minkowski inverse et applications à la théorie locale des espaces normés
V. D. Milman · 1986
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New volume ratio properties for convex symmetric bodies in 𝐑 n {\bf R}^{n}
J. Bourgain and V. D. Milman · 1987
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An estimate for the maximum of the convolution of bounded densities
B. A. Rogozin · 1987
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Logarithmically concave functions and sections of convex sets in 𝐑 n {\bf R}^{n}
K. Ball · 1988
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On the Brunn-Minkowski theorem
H. Groemer · 1988
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Entropy point of view on some geometric inequalities
V. D. Milman · 1988
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Isomorphic symmetrizations and geometric inequalities
V. D. Milman · 1988
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Isotropic position and inertia ellipsoids and zonoids of the unit ball of a normed n n -dimensional space
V. D. Milman and A. Pajor · 1989
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The volume of convex bodies and Banach space geometry
G. Pisier · 1989
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Entropy production by block variable summation and central limit theorems
E. A. Carlen and A. Soffer · 1991
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Information-theoretic inequalities
A. Dembo, T.M. Cover, and J.A. Thomas · 1991
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Characterizations of affinely-rotation-invariant log-concave measures by section-centroid location
M. Meyer and S. Reisner · 1991
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A geometric property of the boundary of symmetric convex bodies and convexity of flotation surfaces
M. Meyer and S. Reisner · 1991
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The Brunn-Minkowski-Firey theory. I. Mixed volumes and the Minkowski problem
E. Lutwak · 1993
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A generalization of the entropy power inequality with applications
R. Zamir and M. Feder · 1993
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On the maximum entropy of the sum of two dependent random variables
T. M. Cover and Z. Zhang · 1994
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Generalized arithmetical progressions and sumsets
I. Z. Ruzsa · 1994
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Volumes of restricted Minkowski sums and the free analogue of the entropy power inequality
S. J. Szarek and D. Voiculescu · 1996
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The inequalities of Fisher information and entropy power for dependent variables
S. Takano · 1996
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Optimal Young’s inequality and its converse: a simple proof
F. Barthe · 1998
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Entropy and a limit theorem for some dependent variables
S. Takano · 1998
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On the volume of the Minkowski sum of line sets and the entropy-power inequality
R. Zamir and M. Feder · 1998
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Restricted Prékopa-Leindler inequality
F. Barthe · 1999
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Shannon’s entropy power inequality via restricted Minkowski sums
S. J. Szarek and D. Voiculescu · 2000
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A short proof of the “concavity of entropy power”
C. Villani · 2000
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A Brunn-Minkowski inequality for the integer lattice
R. J. Gardner and P. Gronchi · 2001
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Gaussian processes: inequalities, small ball probabilities and applications
W. V. Li and Q.-M. Shao · 2001
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An upper bound for d d -dimensional difference sets
Y. V. Stanchescu · 2001
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The Brunn-Minkowski inequality
R. J. Gardner · 2002
Cited alongside, same era.
On solutions to multivariate maximum alpha-entropy problems
J. Costa, A. Hero, and C. Vignat · 2003
Cited alongside, same era.
Some inequalities about mixed volumes
M. Fradelizi, A. Giannopoulos, and M. Meyer · 2003
Cited alongside, same era.
On the rate of convergence in the entropic central limit theorem
S. Artstein, K. M. Ball, F. Barthe, and A. Naor · 2004
Cited alongside, same era.
Solution of Shannon’s problem on the monotonicity of entropy
S. Artstein, K. M. Ball, F. Barthe, and A. Naor · 2004
Cited alongside, same era.
The Santaló point of a function, and a functional form of the Santaló inequality
S. Artstein-Avidan, B. Klartag, and V. Milman · 2004
Cited alongside, same era.
The convex intersection body of a convex body
M. Meyer and S. Reisner · 2011
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Information theoretic proofs of entropy power inequalities
O. Rioul · 2011
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Convexity: An analytic viewpoint
B. Simon · 2011
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Functional affine-isoperimetry and an inverse logarithmic Sobolev inequality
S. Artstein-Avidan, B. Klartag, C. Schütt, and E. Werner · 2012
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Entropy jumps for isotropic log-concave random vectors and spectral gap
K. Ball and V. H. Nguyen · 2012
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Reverse Brunn-Minkowski and reverse entropy power inequalities for convex measures
S. Bobkov and M. Madiman · 2012
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A conditional entropy power inequality for dependent variables
O. Johnson · 2004
Cited alongside, same era.
Fisher information inequalities and the central limit theorem
O. Johnson and A.R. Barron · 2004
Cited alongside, same era.
Information theory and the central limit theorem
Oliver Johnson · 2004
Cited alongside, same era.
Moment-entropy inequalities
E. Lutwak, D. Yang, and G. Zhang · 2004
Cited alongside, same era.
An information-theoretic central limit theorem for finitely susceptible FKG systems
O. Johnson · 2005
Cited alongside, same era.
Geometry of log-concave functions and measures
B. Klartag and V. D. Milman · 2005
Cited alongside, same era.
M. Christ · 2012
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Near equality in the two-dimensional Brunn-Minkowski inequality
M. Christ · 2012
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Entropy and set cardinality inequalities for partition-determined functions
M. Madiman, A. Marcus, and P. Tetali · 2012
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Remark on stability of Brunn-Minkowski and isoperimetric inequalities for convex bodies
A. Segal · 2012
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Rényi divergence and L p L_{p} -affine surface area for convex bodies
E. M. Werner · 2012
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Hadwiger’s Theorem for definable functions
Y. Baryshnikov, R. Ghrist, and M. Wright · 2013
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On the problem of reversibility of the entropy power inequality
S. G. Bobkov and M. M. Madiman · 2013
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Affine moments of a random vector
E. Lutwak, S. Lv, D. Yang, and G. Zhang · 2013
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α \alpha -concave functions and a functional extension of mixed volumes
V. Milman and L. Rotem · 2013
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Mixed integrals and related inequalities
V. Milman and L. Rotem · 2013
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Small ball probability, inverse theorems, and applications
H. H. Nguyen and V. H. Vu · 2013
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Quermassintegrals of quasi-concave functions and generalized Prékopa-Leindler inequalities
S. G. Bobkov, A. Colesanti, and I. Fragalà · 2014
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Divergence for s s -concave and log concave functions
U. Caglar and E. M. Werner · 2014
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On the analogue of the concavity of entropy power in the Brunn-Minkowski theory
M. Fradelizi and A. Marsiglietti · 2014
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The isotropic position and the reverse Santaló inequality
A. Giannopoulos, G. Paouris, and B.-H. Vritsiou · 2014
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A new entropy power inequality for integer-valued random variables
S. Haghighatshoar, E. Abbe, and E. Telatar · 2014
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The entropy power inequality and Mrs. Gerber’s lemma for groups of order 2 n 2^{n}
V. Jog and V. Anantharam · 2014
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The concavity of Rènyi entropy power
G. Savaré and G. Toscani · 2014
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Beyond the entropy power inequality, via rearrangements
L. Wang and M. Madiman · 2014
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A lower bound on the Rényi entropy of convolutions in the integers
L. Wang, J. O. Woo, and M. Madiman · 2014
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Entropies of weighted sums in cyclic groups and an application to polar codes
E. Abbe, J. Li, and M. Madiman · 2015
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On Godbersen’s conjecture
S. Artstein-Avidan, K. Einhorn, D. I. Florentin, and Y. Ostrover · 2015
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A reverse entropy power inequality for log-concave random vectors
K. Ball, P. Nayar, and T. Tkocz · 2015
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A Fourier analytic proof of the Blaschke-Santaló Inequality
G. Bianchi and M. Kelly · 2015
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Entropy power inequality for the Rényi entropy
S. G. Bobkov and G. P. Chistyakov · 2015
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Arak inequalities for concentration functions and the Littlewood–Offord problem
Yu. S. Eliseeva, F. Götze, and A. Yu. Zaitsev · 2015
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Quantitative stability for sumsets in ℝ n \mathbb{R}^{n}
A. Figalli and D. Jerison · 2015
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Concentration of information content for convex measures
M. Fradelizi, J. Li, and M. Madiman · 2015
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On the geometry of convex typical sets
V. Jog and V. Anantharam · 2015
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On sharp bounds for marginal densities of product measures
G. Livshyts, G. Paouris, and P. Pivovarov · 2015
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Entropy bounds on abelian groups and the Ruzsa divergence
M. Madiman and I. Kontoyiannis · 2015
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Sharp isoperimetric inequalities and model spaces for the curvature-dimension-diameter condition
E. Milman · 2015
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A Strengthened Entropy Power Inequality for Log-Concave Densities
G. Toscani · 2015
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A discrete entropy power inequality for uniform distributions
J. O. Woo and M. Madiman · 2015
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Rogers–Shephard inequality for log-concave functions
D. Alonso-Gutiérrez, B. González Merino, C. H. Jiménez, and R. Villa · 2016
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When can one invert Hölder’s inequality? (and why one may want to)
S. Bobkov, M. Fradelizi, J. Li, and M. Madiman · 2016
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Variants of entropy power inequality
S. Bobkov and A. Marsiglietti · 2016
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Log concave functions
A. Colesanti · 2016
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Strengthening the entropy power inequality
T. Courtade · 2016
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Wasserstein Stability of the Entropy Power Inequality for Log-Concave Densities
T. Courtade, M. Fathi, and A. Pananjady · 2016
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Do Minkowski averages get progressively more convex?
M. Fradelizi, M. Madiman, A. Marsiglietti, and A. Zvavitch · 2016
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On the monotonicity of Minkowski sums towards convexity
M. Fradelizi, M. Madiman, A. Marsiglietti, and A. Zvavitch · 2016
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Optimal concentration of information content for log-concave densities
M. Fradelizi, M. Madiman, and L. Wang · 2016
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Information concentration for convex measures
J. Li, M. Fradelizi, and M. Madiman · 2016
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A combinatorial approach to small ball inequalities for sums and differences
J. Li and M. Madiman · 2016
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Combinatorial entropy power inequalities: A preliminary study of the Stam region
M. Madiman and F. Ghassemi · 2016
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Rogozin’s convolution inequality for locally compact groups
M. Madiman, J. Melbourne, and P. Xu · 2016
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Some applications of the nonasymptotic equipartition property of log-concave distributions
M. Madiman, L. Wang, and S. Bobkov · 2016
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On Rényi Entropy Power Inequalities
E. Ram and I. Sason · 2016
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Reverse entropy power inequalities for s s -concave densities
P. Xu, J. Melbourne, and M. Madiman · 2016
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A primer on entropic limit theorems
M. Madiman · 2017
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