Dimensional behaviour of entropy and information
arXiv:1101.3352 · doi:10.1016/j.crma.2011.01.008
Abstract
We develop an information-theoretic perspective on some questions in convex geometry, providing for instance a new equipartition property for log-concave probability measures, some Gaussian comparison results for log-concave measures, an entropic formulation of the hyperplane conjecture, and a new reverse entropy power inequality for log-concave measures analogous to V. Milman's reverse Brunn-Minkowski inequality.
6 pages
References in corpus (3)
Cited by in corpus (20)
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- Beyond the entropy power inequality, via rearrangements
- Forward and Reverse Entropy Power Inequalities in Convex Geometry
- Optimal Concentration of Information Content For Log-Concave Densities
- Entropy bounds on abelian groups and the Ruzsa divergence
- On the problem of reversibility of the entropy power inequality
- Entropy and set cardinality inequalities for partition-determined functions
- Rogozin's convolution inequality for locally compact groups
- Combinatorial Entropy Power Inequalities: A Preliminary Study of the Stam region
- Majorization and Rényi Entropy Inequalities via Sperner Theory
- Sharp moment-entropy inequalities and capacity bounds for log-concave distributions
- Weighted Brunn-Minkowski Theory I: On Weighted Surface Area Measures
- Two remarks on generalized entropy power inequalities
- Concentration of information content for convex measures
- On the volume of the Minkowski sum of zonoids
- Bernoulli sums and Rényi entropy inequalities
- Volumes of subset Minkowski sums and the Lyusternik region
- Entropies of weighted sums in cyclic groups and an application to polar codes
- Entropy jumps for isotropic log-concave random vectors and spectral gap
- Weighted Brunn-Minkowski Theory II: Inequalities for Mixed Measures and Applications