Optimal Concentration of Information Content For Log-Concave Densities
Probability
2019-03-06 v2 Information Theory
Functional Analysis
math.IT
Abstract
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. These bounds significantly improve on the bounds obtained by Bobkov and Madiman ({\it Ann. Probab.}, 39(4):1528--1543, 2011).
Cite
@article{arxiv.1508.04093,
title = {Optimal Concentration of Information Content For Log-Concave Densities},
author = {Matthieu Fradelizi and Mokshay Madiman and Liyao Wang},
journal= {arXiv preprint arXiv:1508.04093},
year = {2019}
}
Comments
15 pages. Changes in v2: Remark 2.5 (due to C. Saroglou) added with more general sufficient conditions for equality in Theorem 2.3. Also some minor corrections and added references