108 citations · 188 across the 30 of their papers we have counts for
36 papers
Stability estimates for the sharp spectral gap bound under a curvature-dimension condition
Max Fathi, Ivan Gentil, Jordan Serres
We study stability of the sharp spectral gap bounds for metric-measure spaces satisfying a curvature bound. Our main result, new even in the smooth setting, is a sharp quantitative…
Time reversal of diffusion processes under a finite entropy condition
Patrick Cattiaux, Giovanni Conforti, Ivan Gentil +1
Motivated by entropic optimal transport, time reversal of diffusion processes is revisited. An integration by parts formula is derived for the carré du champ of a Markov process in…
The entropy, from Clausius to functional inequalities
Ivan Gentil
In this document we are interested in entropy. Entropy is multiple, the idea is to describe the definition proposed by the physicist Clausius. Indeed, Clausius exposes in 1865 the…
Sobolev's inequality under a curvature-dimension condition
Louis Dupaigne, Ivan Gentil, Simon Zugmeyer
In this note we present a new proof of Sobolev's inequality under a uniform lower bound of the Ricci curvature. This result was initially obtained in 1983 by Ilias. Our goal is to…
On the variational interpretation of local logarithmic Sobolev inequalities
Gauthier Clerc, Giovanni Conforti, Ivan Gentil
The celebrated Otto calculus has established itself as a powerful tool for proving quantitative energy dissipation estimates and provides with an elegant geometric interpretation o…
Long-time behaviour of entropic interpolations
Gauthier Clerc, Giovanni Conforti, Ivan Gentil
In this article we investigate entropic interpolations. These measure valued curves describe the optimal solutions of the Schr{ö}dinger problem [Sch31], which is the problem of fin…