Gaussian maximum of entropy and reversed log-Sobolev inequality
Probability
2013-10-23 v1
Abstract
The aim of this note is to connect a reversed form of the Gross logarithmic Sobolev inequality with the Gaussian maximum of Shannon's entropy power. There is thus a complete parallel with the well-known link between logarithmic Sobolev inequalities and their information theoretic counterparts. We moreover provide an elementary proof of the reversed Gross inequality via a two-point inequality and the Central Limit Theorem.
Keywords
Cite
@article{arxiv.math/0102227,
title = {Gaussian maximum of entropy and reversed log-Sobolev inequality},
author = {Djalil Chafai},
journal= {arXiv preprint arXiv:math/0102227},
year = {2013}
}
Comments
6 pages, AMS-LaTeX2e (amsart class)