Modified logarithmic Sobolev inequalities on R

Franck Barthe (1) , Cyril Roberto (2)

1 LSP - Laboratoire de Statistique et Probabilités
2 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

We provide a sufficient condition for a measure on the real line to satisfy a modified logarithmic Sobolev inequality, thus extending the criterion of Bobkov and Götze. Under mild assumptions the condition is also necessary. Concentration inequalities are derived. This completes the picture given in recent contributions by Gentil, Guillin and Miclo.

Domaines: Probabilités [math.PR]

Franck Barthe, Cyril Roberto. Modified logarithmic Sobolev inequalities on R. 2006. ⟨hal-00117472⟩