3 papers
math.ST2025
Sharp comparisons between sliced and standard -Wasserstein distances
Guillaume Carlier, Alessio Figalli, Quentin Mérigot +1
Sliced Wasserstein distances are widely used in practice as a computationally efficient alternative to Wasserstein distances in high dimensions. In this paper, motivated by theoret…
math.AP2024
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…
math.OC2024
Quantitative Stability of the Pushforward Operation by an Optimal Transport Map
Guillaume Carlier, Alex Delalande, Quentin Mérigot
We study the quantitative stability of the mapping that to a measure associates its pushforward measure by a fixed (non-smooth) optimal transport map. We exhibit a tight Hölder-beh…