255 citations · 949 across the 71 of their papers we have counts for
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Weak logarithmic Sobolev inequalities and entropic convergence
Patrick Cattiaux, Ivan Gentil, Arnaud Guillin
In this paper we introduce and study a weakened form of logarithmic Sobolev inequalities in connection with various others functional inequalities (weak Poincaré inequalities, gene…
Modified logarithmic Sobolev inequalities in null curvature
Ivan Gentil, Arnaud Guillin, Laurent Miclo
We present a logarithmic Sobolev inequality adapted to a log-concave measure. Assume that is a symmetric convex function on $\dR$ satisfying $(1+\e)Φ(x)\leq {x}Φ'(x)\leq(2-\e)Φ…
Quantitative concentration inequalities for empirical measures on non-compact spaces
Francois Bolley, Arnaud Guillin, Cedric Villani
We establish some quantitative concentration estimates for the empirical measure of many independent variables, in transportation distances. As an application, we provide some erro…
Examples of moderate deviation principle for diffusion processes
A. Guillin, R. Liptser
Taking into account some likeness of moderate deviations (MD) and central limit theorems (CLT), we develop an approach, which made a good showing in CLT, for MD analysis of a famil…