68 citations · 321 across the 52 of their papers we have counts for
61 papers
On Optimal Transport Maps Between 1 /d-Concave Densities
Guillaume Carlier, Alessio Figalli, Filippo Santambrogio
In this paper, we extend the scope of Caffarelli's contraction theorem, which provides a measure of the Lipschitz constant for optimal transport maps between log-concave probabilit…
New Lipschitz estimates and long-time asymptotic behavior for porous medium and fast diffusion equations
Noemi David, Filippo Santambrogio
We obtain new estimates for the solution of both the porous medium and the fast diffusion equations by studying the evolution of suitable Lipschitz norms. Our results include insta…
Uniform contractivity of the Fisher infinitesimal model with strongly convex selection
Vincent Calvez, David Poyato, Filippo Santambrogio
The Fisher infinitesimal model is a classical model of phenotypic trait inheritance in quantitative genetics. Here, we prove that it encompasses a remarkable convexity structure wh…
Strong convergence of the JKO scheme for the Fokker-Planck equation
Filippo Santambrogio, Gayrat Toshpulatov
Following a celebrated paper by Jordan, Kinderleherer and Otto it is possible to discretize in time the Fokker-Planck equation b…
A cross-diffusion system obtained via (convex) relaxation in the JKO scheme
Romain Ducasse, Filippo Santambrogio, Havva Yoldaş
In this paper, we start from a very natural system of cross-diffusion equations, which can be seen as a gradient flow for the Wasserstein distance of a certain functional. Unfortun…
Non-asymptotic convergence bounds for Wasserstein approximation using point clouds
Quentin Merigot, Filippo Santambrogio, Clément Sarrazin
Several issues in machine learning and inverse problems require to generate discrete data, as if sampled from a model probability distribution. A common way to do so relies on the…