Almost sharp rates of convergence for the average cost and displacement in the optimal matching problem
Analysis of PDEs
2023-12-14 v1 Mathematical Physics
math.MP
Probability
Abstract
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.
Keywords
Cite
@article{arxiv.2312.07995,
title = {Almost sharp rates of convergence for the average cost and displacement in the optimal matching problem},
author = {Michael Goldman and Martin Huesmann and Felix Otto},
journal= {arXiv preprint arXiv:2312.07995},
year = {2023}
}