Gaussian maximum of entropy and reversed log-Sobolev inequality
arXiv:math/0102227 · doi:10.1007/978-3-540-36107-7_5
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.
6 pages, AMS-LaTeX2e (amsart class)