arXiv subjects
Publications and source records attributed to Patrick Cattiaux.
$μ$ being a nonnegative measure satisfying some log-Sobolev inequality, we give conditions on F for the measure $ν=e^{-2F} μ$ to also satisfy some log-Sobolev inequality. Explicit examples are studied.
If a random variable is not exponentially integrable, it is known that no concentration inequality holds for an infinite sequence of independent copies. Under mild conditions, we establish concentration inequalities for finite sequences of $n$ independent copies, with good dependence in $n$.
We show that the quadratic transportation cost inequality $T_2$ is equivalent to both a Poincaré inequality and a strong form of the Gaussian concentration property. The main ingredient in the proof is a new family of inequalities, called modified quadratic transportation cost inequalities in the spirit of the modified logarithmic-Sobolev inequalities by Bobkov and Ledoux \cite{BL97}, that are shown to hold as soon as a Poincaré inequality is satisfied.