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This work studies the quantitative stability of the quadratic optimal transport map between a fixed probability density $\rho$ and a probability measure $\mu$ on R^d , which we denote T$\mu$.
Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert
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Elsa Cazelles, Vivien Seguy, Jérémie Bigot, Marco Cuturi, and Nicolas Papadakis · 2018
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Representing and learning high dimensional data with the optimal transport map from a probabilistic viewpoint
S. Park and M. Thorpe · 2018
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High-Dimensional Probability: An Introduction with Applications in Data Science
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Quantitative Stability of Barycenters in the Wasserstein Space
Guillaume Carlier, Alex Delalande, and Quentin Merigot · 2022
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