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math.AP2024
Gluing methods for quantitative stability of optimal transport maps
Cyril Letrouit, Quentin Mérigot
We establish quantitative stability bounds for the quadratic optimal transport map between a fixed probability density and a probability measure on . Un…
physics.comp-ph2024
Large-scale semi-discrete optimal transport with distributed Voronoi diagrams
Bruno Lévy, Nicolas Ray, Quentin Mérigot +1
In this article, we propose a numerical method to solve semi-discrete optimal transport problems for gigantic pointsets (108 points and more). By pushing the limits by several orde…
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…