A PROOF OF THE CAFFARELLI CONTRACTION THEOREM VIA ENTROPIC REGULARIZATION
Résumé
We give a new proof of the Caffarelli contraction theorem, which states that the Brenier optimal transport map sending the standard Gaussian measure onto a uniformly log-concave probability measure is Lipschitz. The proof combines a recent variational characterization of Lipschitz transport map by the second author and Juillet with a convexity property of optimizers in the dual formulation of the entropy-regularized optimal transport (or Schrödinger) problem.
| Origine | Fichiers produits par l'(les) auteur(s) |
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