Bounds on the deficit in the logarithmic Sobolev inequality

Sergey Bobkov (1) , Nathael Gozlan (2) , Cyril Roberto (3) , Paul-Marie Samson (2)

1 UMN-MATH - School of Mathematics
2 Laboratoire d'Analyse et de Mathématiques Appliquées
3 MODAL'X - Modélisation aléatoire de Paris X

The de cit in the logarithmic Sobolev inequality for the Gaussian measure is considered and estimated by means of transport and information-theoretic distances.

Mots clés: Entropy; Logarithmic Sobolev inequality; Fisher Information; Transport Distance; Gaussian measure

Domaines: Probabilités [math.PR]; Analyse fonctionnelle [math.FA]

Sergey Bobkov, Nathael Gozlan, Cyril Roberto, Paul-Marie Samson. Bounds on the deficit in the logarithmic Sobolev inequality. Journal of Functional Analysis, 2014, 267 (11), pp.4110-4138. ⟨hal-01053507⟩