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Pré-Publication, Document De Travail Année : 2024

On optimal transport maps between 1/d-concave densities

Résumé

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 probability densities in $\R^d$. Our focus is on a broader category of densities, specifically those that are $\nicefrac{1}{d}$-concave and can be represented as $V^{-d}$, where $V$ is convex. By setting appropriate conditions, we derive linear or sublinear limitations for the optimal transport map. This leads us to a comprehensive Lipschitz estimate that aligns with the principles established in Caffarelli's theorem.
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Dates et versions

hal-04534818 , version 1 (05-04-2024)

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  • HAL Id : hal-04534818 , version 1

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Guillaume Carlier, Alessio Figalli, Filippo Santambrogio. On optimal transport maps between 1/d-concave densities. 2024. ⟨hal-04534818⟩
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