Calculus of Variations and Geometric Measure Theory

M. Goldman - M. Huesmann - F. Otto

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

created by goldman on 13 Dec 2023

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Inserted: 13 dec 2023
Last Updated: 13 dec 2023

Year: 2023

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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