Gaussian maximum of entropy and reversed log-Sobolev inequality

Details Gaussian maximum of entropy and reversed log-Sobolev inequality Gaussian maximum of entropy and reversed log-Sobolev inequality

2001-02-28

arxiv.org/abs/math/0102227v1

Mathematics

Probability

6 pages, AMS-LaTeX2e (amsart class)

Scientific paper

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.

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