Fetching the paper…
Reading the bibliography…
An elementary proof is provided of sharp bounds for the varentropy of random vectors with log-concave densities, as well as for deviations of the information content from its mean.
Probability inequalities for the sum of independent random variables
G. Bennett · 1962
Earlier work this paper cites.
Convex analysis
R. T. Rockafellar · 1970
Earlier work this paper cites.
Complements of Lyapunov’s inequality
C. Borell · 1973
Earlier work this paper cites.
On logarithmic concave measures and functions
A. Prékopa · 1973
Earlier work this paper cites.
Limit theorems for the ratio of the empirical distribution function to the true distribution function
J. A. Wellner · 1978
Earlier work this paper cites.
Convex analysis and minimization algorithms. I
J.-B. Hiriart-Urruty and C. Lemaréchal · 1993
Earlier work this paper cites.
Sections of convex bodies through their centroid
M. Fradelizi · 1997
Earlier work this paper cites.
Analysis
E. H. Lieb and M. Loss · 2001
Earlier work this paper cites.
Convex optimization
S. Boyd and L. Vandenberghe · 2004
Earlier work this paper cites.
Geometry of log-concave functions and measures
B. Klartag and V. D. Milman · 2005
Earlier work this paper cites.
A central limit theorem for convex sets
B. Klartag · 2007
Earlier work this paper cites.
Increasing functions and inverse Santaló inequality for unconditional functions
M. Fradelizi and M. Meyer · 2008
Earlier work this paper cites.
Reinforcement of an inequality due to Brascamp and Lieb
G. Hargé · 2008
Cited alongside, same era.
Concentration of the information in data with log-concave distributions
S. Bobkov and M. Madiman · 2011
Cited alongside, same era.
Dimensional behaviour of entropy and information
S. Bobkov and M. Madiman · 2011
Cited alongside, same era.
The entropy per coordinate of a random vector is highly constrained under convexity conditions
S. Bobkov and M. Madiman · 2011
Cited alongside, same era.
Approximately gaussian marginals and the hyperplane conjecture
R. Eldan and B. Klartag · 2011
Cited alongside, same era.
Interpolating thin-shell and sharp large-deviation estimates for isotropic log-concave measures
O. Guédon and E. Milman · 2011
Cited alongside, same era.
Volume of the polar of random sets and shadow systems
D. Cordero-Erausquin, M. Fradelizi, G. Paouris, and P. Pivovarov · 2014
Later among the works it cites.
Bounding the norm of a log-concave vector via thin-shell estimates
R. Eldan and J. Lehec · 2014
Later among the works it cites.
Dimensional variance inequalities of Brascamp-Lieb type and a local approach to dimensional Prékopa’s theorem
V. H. Nguyen · 2014
Later among the works it cites.
Heat capacity bound, energy fluctuations and convexity
L. Wang · 2014
Later among the works it cites.
Beyond the entropy power inequality, via rearrangements
L. Wang and M. Madiman · 2014
Later among the works it cites.
When can one invert Hölder’s inequality? (and why one may want to)
S. Bobkov, M. Fradelizi, and M. Madiman · 2015
Closest in time.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
A local maximal inequality under uniform entropy
A. van der Vaart and J. A. Wellner · 2011
Cited alongside, same era.
Reverse Brunn-Minkowski and reverse entropy power inequalities for convex measures
S. Bobkov and M. Madiman · 2012
Cited alongside, same era.
Concentration inequalities
S. Boucheron, G. Lugosi, and P. Massart · 2013
Cited alongside, same era.
Thin shell implies spectral gap up to polylog via a stochastic localization scheme
R. Eldan · 2013
Cited alongside, same era.
Inégalités fonctionnelles et convexité
V. H. Nguyen · 2013
Cited alongside, same era.
Dimensional improvements of the logarithmic sobolev, talagrand and brascamp-lieb inequalities
F. Bolley, I. Gentil, and A. Guillin · 2015
Closest in time.
Concentration of information content and other functionals under convex measures
M. Fradelizi, J. Li, and M. Madiman · 2015
Closest in time.
Eigenvalue distribution of optimal transportation
B. Klartag · 2015
Closest in time.
Eigenvalue distribution of optimal transportation
B. Klartag and A. Kolesnikov · 2015
Closest in time.
Some applications of the nonasymptotic equipartition property of log-concave distributions
M. Madiman, L. Wang, and S. Bobkov · 2015
Closest in time.