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 $\Phi$ is a symmetric convex function on $\dR$ satisfying $(1+\e)Φ(x)\leq {x}Φ'(x)\leq(2-\e)Φ…