6 papers
Quantitative stability in distribution for the Sobolev inequality under curvature dimension condition
Max Fathi, Ivan Yuri Violo
The goal of this note is to investigate quantitative stability properties of the critical Sobolev inequality in metric measure spaces. Assuming that the optimal c…
Quantitative rigidity of the Wasserstein contraction under convolution
Max Fathi, Michael Goldman, Daniel Tsodyks
The aim of this paper is to investigate the contraction properties of -Wasserstein distances with respect to convolution in Euclidean spaces both qualitatively and quantitativel…
Stochastic proof of the sharp symmetrized Talagrand inequality
Thomas A. Courtade, Max Fathi, Dan Mikulincer
We give a new proof of the sharp symmetrized form of Talagrand's transport-entropy inequality. Compared to stochastic proofs of other Gaussian functional inequalities, the new idea…
Stability of the Poincaré-Korn inequality
Thomas A. Courtade, Max Fathi
We resolve a question of Carrapatoso et al. on Gaussian optimality for the sharp constant in Poincaré-Korn inequalities, under a moment constraint. We also prove stability, showing…
Stability of Klartag's improved Lichnerowicz inequality
Thomas A. Courtade, Max Fathi
In a recent work, Klartag gave an improved version of Lichnerowicz' spectral gap bound for uniformly log-concave measures, which improves on the classical estimate by taking into a…
HWI inequalities in discrete spaces via couplings
Thomas A. Courtade, Max Fathi
HWI inequalities are interpolation inequalities relating entropy, Fisher information and optimal transport distances. We adapt an argument of Y. Wu for proving the Gaussian HWI ine…