Modified logarithmic Sobolev inequalities in null curvature

Ivan Gentil (1) , Arnaud Guillin (1) , Laurent Miclo (2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 LATP - Laboratoire d'Analyse, Topologie, Probabilités

We present a new logarithmic Sobolev inequality adapted to a log-concave measure on $\dR$ between the exponential and the Gaussian measure.

Mots clés: Log-concave Measure; Logarithmic Sobolev inequality; Poincaré inequality; Concentration inequality; Log-concave Measure.

Domaines: Probabilités [math.PR]

Ivan Gentil, Arnaud Guillin, Laurent Miclo. Modified logarithmic Sobolev inequalities in null curvature. Revista Matemática Iberoamericana, 2007, 23 (1), pp.237-260. ⟨hal-00016868v2⟩