A proof of the Caffarelli contraction theorem via entropic regularization

By Max Fathi, Nathael Gozlan, Maxime Prod’homme. Calculus of Variations and Partial Differential Equations, 2019

54 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/b16e223019c2310ad83159cfd39e2d3fb1e81f2d

Citations in the corpus

• Stability of martingale optimal transport and weak optimal transport (2019, unknown): “We also refer to [25, 21] for some unexpected applications of weak transport problems in analysis and probability.”