On optimal transport maps between $\frac{1}{d}$-concave densities
Year: 2024
Type: article
Abstract: 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 \mathbb{R}^{d} . Our focus is on a broader category of densities, specifically those that are \frac{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.
DOI: 10.4171/aihpc/148
Institutions: Institut national de recherche en sciences et technologies du numérique, Université Paris Dauphine-PSL, ETH Zurich, Lyon 1 Université, École Centrale de Lyon, Centre National de la Recherche Scientifique, Institut Camille Jordan, Université Jean Monnet, Institut National des Sciences Appliquées de Lyon, Université Jean Monnet
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $700
OpenAlex ID: W4404137447