Gaussian maximum of entropy and reversed log-Sobolev inequality

Djalil Chafai (1)

1 LSP - Laboratoire de Statistique et Probabilités

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.

Domaines: Probabilités [math.PR]

Djalil Chafai. Gaussian maximum of entropy and reversed log-Sobolev inequality. Séminaire de Probabilités XXXVI, 2003, Lecture Notes in Mathematics 1801, pp.194--200. ⟨10.1007/b10068⟩. ⟨hal-00180775⟩