Bounds on optimal transport maps onto log-concave measures

We consider strictly log-concave measures, whose bounds degenerate at infinity. We prove that the optimal transport map from the Gaussian onto such a measure is locally Lipschitz, and that the eigenvalues of its Jacobian have controlled growth at infinity. (C) 2020 Elsevier Inc. All rights reserved.

Automated summary

The article focuses on strictly log-concave measures and Gaussian distributions, discussing the optimal transport map between them and proving some properties of this mapping.