Stein’s method, logarithmic Sobolev and transport inequalities

Modified logarithmic Sobolev inequalities and transportation inequalities

Logarithmic Sobolev, Isoperimetry and Transport Inequalities on Graphs

In this paper, we study some functional inequalities (such as Poincaré inequality, logarithmic Sobolev inequality, generalized Cheeger isoperimetric inequality, transportation-information inequality and transportation-entropy inequality) for reversible nearest-neighbor Markov processes on connected finite graphs by means of (random) path method. We provide estimates of the involved constants.

Weak logarithmic Sobolev inequalities and entropic convergence

In this paper we introduce and study a weakened form of logarithmic Sobolev inequalities in connection with various others functional inequalities (weak Poincaré inequalities, general Beckner inequalities...). We also discuss the quantitative behaviour of relative entropy along a symmetric diffusion semi-group. In particular, we exhibit an example where Poincaré inequality can not be used for d...

Isoperimetry and Symmetrization for Logarithmic Sobolev Inequalities

Using isoperimetry and symmetrization we provide a unified framework to study the classical and logarithmic Sobolev inequalities. In particular, we obtain new Gaussian symmetrization inequalities and connect them with logarithmic Sobolev inequalities. Our methods are very general and can be easily adapted to more general contexts.

Logarithmic Sobolev Inequalities and the Information Theory

In this paper we present an overview on logarithmic Sobolev inequalities. These inequalities have become a subject of intense research activity during the past years, from analysis and geometry in finite and infinite dimension, to probability and statistical mechanics, and of course many others developments and applications are expected. We have divided this paper into three parts. The first pa...