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arXiv · 2401.01088

Quantitative Stability of the Pushforward Operation by an Optimal Transport Map

Guillaume Carlier·Alex Delalande·Quentin Mérigot
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Abstract

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 H\"older-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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Guillaume Carlier, Alex Delalande, Quentin Mérigot. 2024-01-02. Quantitative Stability of the Pushforward Operation by an Optimal Transport Map. https://arxiv.org/abs/2401.01088

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