A note on Talagrand's transportation inequality and logarithmic Sobolev inequality

Patrick Cattiaux (1) , Arnaud Guillin (2, 3) , Li-Ming Wu

1 LSP - Laboratoire de Statistique et Probabilités
2 LMBP - Laboratoire de Mathématiques Blaise Pascal
3 LMBP - Laboratoire de Mathématiques Blaise Pascal

We give by simple arguments sufficient conditions, so called Lyapunov conditions, for Talagrand's transportation information inequality and for the logarithmic Sobolev inequality. Those sufficient conditions work even in the case where the Bakry-Emery curvature is not lower bounded. Several new examples are provided.

Mots clés: Lyapunov functions; Talagrand transportation information inequality; logarithmic Sobolev inequality

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

Patrick Cattiaux, Arnaud Guillin, Li-Ming Wu. A note on Talagrand's transportation inequality and logarithmic Sobolev inequality. Probability Theory and Related Fields, 2010, 148 (1-2), pp.285-304. ⟨10.1007/s00440-009-0231-9⟩. ⟨hal-00335566⟩