In this work, we consider dimensional improvements of the logarithmic Sobolev, Talagrand
and Brascamp–Lieb inequalities. For this, we use optimal transport methods and the Borell …

In this paper, we offer a proof for a family of functional inequalities interpolating between the
Poincaré and the logarithmic Sobolev (standard and weighted) inequalities. The proofs rely …

We consider elliptic diffusion processes on R d. Assuming that the drift contracts distances
outside a compact set, we prove that, when the diffusion coefficient is sufficiently large, the …

Weighted Poincare inequalities, concentration inequalities and tail bounds related to Stein
kernels in dimension one Page 1 Bernoulli 25(4B), 2019, 3978–4006 https://doi.org/10.3150/19-BEJ1117 …

We study Poincaré inequalities and long-time behavior for diffusion processes on R n under
a variable curvature lower bound, in the sense of Bakry-Emery. We derive various estimates …

We consider elliptic diffusion processes on $\mathbb R^ d $. Assuming that the drift
contracts distances outside a compact set, we prove that, at a sufficiently high temperature …

Using some harmonic extensions on the upper-half plane, and probabilistic representations,
and curvature-dimension inequalities with some negative dimensions, we obtain some new …

This note presents a method based on Feynman-Kac semigroups for logarithmic Sobolev
inequalities. It follows the recent work of Bonnefont and Joulin on intertwining relations for …

Dealing with one-dimensional diffusion operators, we obtain upper and lower variational
formulae on the eigenvalues given by the max–min principle, generalizing the celebrated …

We explore the consequences of the so-called intertwinings between gradients and Markov
diffusion operators on $ R^ d $ in terms of second-order Brascamp-Lieb inequalities for log …