Some remarks on weighted logarithmic Sobolev inequality

Patrick Cattiaux (1) , Arnaud Guillin (2) , Liming Wu (2, 3)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 LMBP - Laboratoire de Mathématiques Blaise Pascal
3 Institute of Applied Mathematics

We give here a simple proof of weighted logarithmic Sobolev inequality, for example for Cauchy type measures, with optimal weight, sharpening results of Bobkov-Ledoux. Some consequences are also discussed.

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

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

Patrick Cattiaux, Arnaud Guillin, Liming Wu. Some remarks on weighted logarithmic Sobolev inequality. Indiana University Mathematics Journal, 2011, 60 (6), pp.1885-1904. ⟨hal-00485124⟩