Some recent developments in functional inequalities

Emmanuel Boissard (1) , Nathael Gozlan (2) , Joseph Lehec (3) , Christian Léonard (4) , Georg Menz (5) , André Schlichting (6)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
3 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
4 MODAL'X - Modélisation aléatoire de Paris X
5 Department of Mathematics [UCLA]
6 Department of Mathematics - University of Bonn

This paper presents different recent directions in the study of some classical functional inequalities: the Poincaré inequality, the logarithmic Sobolev inequality and Talagrand's quadratic transport-entropy inequality. The results presented in this text were the subjects of a series of talks given by the authors in the session ``Functional inequalities'' during the Journées MAS 2012 in Clermont-Ferrand.

Domaines: Probabilités [math.PR]

Emmanuel Boissard, Nathael Gozlan, Joseph Lehec, Christian Léonard, Georg Menz, et al.. Some recent developments in functional inequalities. Journées MAS 2012 - Concentration et application, Aug 2012, Clermont-Ferrand, France. pp.338-354, ⟨10.1051/proc/201444021⟩. ⟨hal-01273139⟩