Some recent developments in functional inequalities

Abstract

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.