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Gaussian maximum of entropy and reversed log-Sobolev inequality

Djalil Chafai
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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.

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Djalil Chafai. 2001-02-28. Gaussian maximum of entropy and reversed log-Sobolev inequality. https://doi.org/10.1007/978-3-540-36107-7_5

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