Stability for the logarithmic Sobolev inequality

Giovanni Brigati (1) , Jean Dolbeault (1) , Nikita Simonov (2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions

This paper is devoted to stability results for the Gaussian logarithmic Sobolev inequality. Our approach covers several cases involving the strongest possible norm with the optimal exponent, under constraints. Explicit constants are obtained. The strategy of proof relies on entropy methods and the Ornstein-Uhlenbeck flow.

Mots clés: Logarithmic Sobolev inequality; stability; log-concavity; heat flow; entropy; carré du champ

Domaines: Mathématiques [math]

Giovanni Brigati, Jean Dolbeault, Nikita Simonov. Stability for the logarithmic Sobolev inequality. 2023. ⟨hal-04042046v1⟩