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arXiv · 2312.07995

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

Michael Goldman·Martin Huesmann·Felix Otto
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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.

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Michael Goldman, Martin Huesmann, Felix Otto. 2023-12-13. Almost sharp rates of convergence for the average cost and displacement in the optimal matching problem. https://arxiv.org/abs/2312.07995

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