Almost sharp rates of convergence for the average cost and displacement in the optimal matching problem

Autor:	Goldman, Michael, Huesmann, Martin, Otto, Felix
Rok vydání:	2023
Předmět:	Mathematics - Analysis of PDEs Mathematical Physics Mathematics - Probability
Druh dokumentu:	Working Paper
Popis:	In this note we prove estimates for the average cost in the quadratic optimal transport problem on the two-dimensional flat torus which are optimal up to a double logarithm. We also prove sharp estimates on the displacement. This is based on the combination of a post-processing of our quantitative linearization result together with a quasi-orthogonality property.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2312.07995 Zobrazit plný text záznamu View this record from Arxiv