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Pré-Publication, Document De Travail Année : 2023

Quantitative Stability of the Pushforward Operation by an Optimal Transport Map

Résumé

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-behavior for this operation under minimal assumptions. Our proof essentially relies on a new bound that quantifies the size of the singular sets of a convex and Lipschitz continuous function on a bounded domain.
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Dates et versions

hal-04368103 , version 1 (31-12-2023)

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  • HAL Id : hal-04368103 , version 1

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Guillaume Carlier, Alex Delalande, Quentin Mérigot. Quantitative Stability of the Pushforward Operation by an Optimal Transport Map. 2023. ⟨hal-04368103⟩
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