From the 2 of 5 linked papers with an AI index.
5 papers
A Brenier-Strassen Theorem on CAT(kappa) Spaces
Nathael Gozlan, Hugo Malamut, Shin-Ichi Ohta
The paper generalizes the Brenier‑Strassen theorem to spaces with curvature bounded above, proving existence and uniqueness of a Wasserstein‑2 projection onto measures dominated in…
Computing Barycentres of Measures for Generic Transport Costs
Eloi Tanguy, Julie Delon, Nathaël Gozlan
The paper proposes and analyzes a fixed‑point algorithm for computing barycentres of probability measures under general transport costs, providing convergence guarantees and numeri…
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…
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.
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…