86 citations · 350 across the 38 of their papers we have counts for
40 papers
Functional inequalities along Wasserstein geodesics
Nathael Gozlan, Hugo Malamut, Irène Waldspurger
We study functional inequalities along Wasserstein geodesics. If 0 and 1 are respectively 0 -and 1 -strongly log-concave probability measures on R n , we prove that…
A Brenier-Strassen Theorem on CAT(kappa) Spaces
Nathael Gozlan, Hugo Malamut, Shin-Ichi Ohta
We extend the Brenier-Strassen theorem about projections in convex order to non-flat spaces with curvature bounded from above. Precisely, for probability measures , of finit…
On the quadratic barycentric transport problem
Nathael Gozlan, Thibaut Le Gouic, Paul-Marie Samson
We investigate the structure of optimal transport plans, dual optimizers, and geodesic paths for the quadratic barycentric transport problem.
Global Regularity Estimates for Optimal Transport via Entropic Regularisation
Nathael Gozlan, Maxime Sylvestre
We develop a general approach to prove global regularity estimates for quadratic optimal transport using the entropic regularisation of the problem and the Prekopa-Leindler inequal…
Computing Barycentres of Measures for Generic Transport Costs
Eloi Tanguy, Julie Delon, Nathaël Gozlan
Wasserstein barycentres represent average distributions between multiple probability measures for the Wasserstein distance. The numerical computation of Wasserstein barycentres is…
Duality and Heat flow
Dario Cordero-Erausquin, Nathael Gozlan, Shohei Nakamura +1
We reveal the relation between the Legendre transform of convex functions and heat flow evolution, and how it applies to the functional Blaschke-Santalo inequality. We also describ…