Fetching the paper…
Reading the bibliography…
We develop a reverse entropy power inequality for convex measures, which may be seen as an affine-geometric inverse of the entropy power inequality of Shannon and Stam.
Verallgemeinerung eines Mittelwertsatzes von J. Favard für positive konkave Funktionen
L. Berwald · 1947
Earlier work this paper cites.
A mathematical theory of communication
C.E. Shannon · 1948
Earlier work this paper cites.
Brunn-Minkowskischer Satz und Isoperimetrie
H. Hadwiger and D. Ohmann · 1956
Earlier work this paper cites.
The difference body of a convex body
C. A. Rogers and G. C. Shephard · 1957
Earlier work this paper cites.
Convex bodies associated with a given convex body
C. A. Rogers and G. C. Shephard · 1958
Earlier work this paper cites.
Some inequalities satisfied by the quantities of information of Fisher and Shannon
A.J. Stam · 1959
Earlier work this paper cites.
Eine zahlentheoretische Anwendung der Graphentheorie
H. Plünnecke · 1970
Earlier work this paper cites.
Logarithmic concave measures with application to stochastic programming
A. Prékopa · 1971
Earlier work this paper cites.
Complements of Lyapunov’s inequality
C. Borell · 1973
Earlier work this paper cites.
Convex measures on locally convex spaces
C. Borell · 1974
Earlier work this paper cites.
Convex set functions in d d -space
C. Borell · 1975
Earlier work this paper cites.
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
Earlier work this paper cites.
On the similarity of the entropy power inequality and the Brunn-Minkowski inequality
M.H.M. Costa and T.M. Cover · 1984
Earlier work this paper cites.
A new entropy power inequality
M.H.M. Costa · 1985
Earlier work this paper cites.
Isometric problems in ℓ p \ell^{p} and sections of convex sets
K. Ball · 1986
Earlier work this paper cites.
Inégalité de Brunn-Minkowski inverse et applications à la théorie locale des espaces normés
V. D. Milman · 1986
Earlier work this paper cites.
Logarithmically concave functions and sections of convex sets in 𝐑 n {\bf R}^{n}
K. Ball · 1988
Earlier work this paper cites.
Geometric inequalities
Yu. D. Burago and V. A. Zalgaller · 1988
Earlier work this paper cites.
Entropy point of view on some geometric inequalities
V. D. Milman · 1988
Cited alongside, same era.
Isomorphic symmetrizations and geometric inequalities
V. D. Milman · 1988
Cited alongside, same era.
Simple proof of the concavity of the entropy power with respect to added Gaussian noise
A. Dembo · 1989
Cited alongside, same era.
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
Cited alongside, same era.
The volume of convex bodies and Banach space geometry
G. Pisier · 1989
Cited alongside, same era.
An application of graph theory to additive number theory
I. Z. Ruzsa · 1989
Cited alongside, same era.
Large deviations and isoperimetry over convex probability measures with heavy tails
S. G. Bobkov · 2007
Later among the works it cites.
A central limit theorem for convex sets
B. Klartag · 2007
Later among the works it cites.
Generalized entropy power inequalities and monotonicity properties of information
M. Madiman and A.R. Barron · 2007
Later among the works it cites.
The M M -ellipsoid, symplectic capacities and volume
S. Artstein-Avidan, V. Milman, and Y. Ostrover · 2008
Later among the works it cites.
Increasing functions and inverse Santaló inequality for unconditional functions
M. Fradelizi and M. Meyer · 2008
Later among the works it cites.
Plünnecke’s inequality for different summands
K. Gyarmati, M. Matolcsi, and I. Z. Ruzsa · 2008
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Information-theoretic inequalities
A. Dembo, T.M. Cover, and J.A. Thomas · 1991
Cited alongside, same era.
Volumes of restricted Minkowski sums and the free analogue of the entropy power inequality
S. J. Szarek and D. Voiculescu · 1996
Cited alongside, same era.
Sections of convex bodies through their centroid
M. Fradelizi · 1997
Cited alongside, same era.
Entropy and asymptotic geometry of non-symmetric convex bodies
V. D. Milman and A. Pajor · 2000
Cited alongside, same era.
Shannon’s entropy power inequality via restricted Minkowski sums
S. J. Szarek and D. Voiculescu · 2000
Cited alongside, same era.
A short proof of the “concavity of entropy power”
C. Villani · 2000
Cited alongside, same era.
On the entropy of sums
M. Madiman · 2008
Later among the works it cites.
Product set estimates for non-commutative groups
T. Tao · 2008
Later among the works it cites.
A Freĭman-type theorem for locally compact abelian groups
T. Sanders · 2009
Later among the works it cites.
Convex bodies and norms associated to convex measures
S. G. Bobkov · 2010
Later among the works it cites.
When can one invert Hölder’s inequality? (and why one may want to)
S. G. Bobkov and M. Madiman · 2010
Later among the works it cites.
Dimensional behaviour of entropy and information
S. Bobkov and M. Madiman · 2011
Closest in time.
On the problem of reversibility of the entropy power inequality
S. Bobkov and M. Madiman · 2011
Closest in time.
On Milman’s ellipsoids and M M -position of convex bodies
S. G. Bobkov · 2011
Closest in time.
Concentration of the information in data with log-concave distributions
S. G. Bobkov and M. Madiman · 2011
Closest in time.
The entropy per coordinate of a random vector is highly constrained under convexity conditions
S. G. Bobkov and M. Madiman · 2011
Closest in time.
Entropy and set cardinality inequalities for partition-determined functions
M. Madiman, A. Marcus, and P. Tetali · 2011
Closest in time.