Almost Sharp Rates of Convergence for the Average Cost and Displacement in the Optimal Matching Problem

Michael Goldman; Martin Huesmann; Felix Otto

doi:10.1007/978-3-031-91282-5_5

Almost Sharp Rates of Convergence for the Average Cost and Displacement in the Optimal Matching Problem

Michael Goldman
, Martin Huesmann
, Felix Otto

University of Münster
Max Planck Institute for Mathematics in the Sciences

Résultats de recherche: Le chapitre dans un livre, un rapport, une anthologie ou une collection › Contribution à une conférence › Revue par des pairs

Résumé

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.

langue originale	Anglais
titre	Partial Differential Equations
Sous-titre	Waves, Nonlinearities and Nonlocalities - The Abel Symposium 2023
rédacteurs en chef	Mats Ehrnström, Helge Holden, Espen R. Jakobsen
Editeur	Springer Science and Business Media Deutschland GmbH
Pages	93-109
Nombre de pages	17
ISBN (imprimé)	9783031912818
Les DOIs	https://doi.org/10.1007/978-3-031-91282-5_5
état	Publié - 1 janv. 2025
Evénement	Abel Symposium on Partial Differential Equations: Waves, Nonlinearities and Nonlocalities, 2023 - Orkanger, Norvcge Durée: 13 juin 2023 → 16 juin 2023

Série de publications

Nom	Abel Symposia
Volume	18 ABEL
ISSN (imprimé)	2193-2808
ISSN (Electronique)	2197-8549

Une conférence

Une conférence	Abel Symposium on Partial Differential Equations: Waves, Nonlinearities and Nonlocalities, 2023
Pays/Territoire	Norvcge
La ville	Orkanger
période	13/06/23 → 16/06/23

Accès au document

10.1007/978-3-031-91282-5_5

Autres fichiers et liens

Lien vers la publication dans Scopus

Contient cette citation

Goldman, M., Huesmann, M., & Otto, F. (2025). Almost Sharp Rates of Convergence for the Average Cost and Displacement in the Optimal Matching Problem. Dans M. Ehrnström, H. Holden, & E. R. Jakobsen (eds.), Partial Differential Equations: Waves, Nonlinearities and Nonlocalities - The Abel Symposium 2023 (p. 93-109). (Abel Symposia; Vol 18 ABEL). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-91282-5_5

Goldman, Michael ; Huesmann, Martin ; Otto, Felix. / Almost Sharp Rates of Convergence for the Average Cost and Displacement in the Optimal Matching Problem. Partial Differential Equations: Waves, Nonlinearities and Nonlocalities - The Abel Symposium 2023. Editeur / Mats Ehrnström ; Helge Holden ; Espen R. Jakobsen. Springer Science and Business Media Deutschland GmbH, 2025. p. 93-109 (Abel Symposia).

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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.",

author = "Michael Goldman and Martin Huesmann and Felix Otto",

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Goldman, M, Huesmann, M & Otto, F 2025, Almost Sharp Rates of Convergence for the Average Cost and Displacement in the Optimal Matching Problem. Dans M Ehrnström, H Holden & ER Jakobsen (eds), Partial Differential Equations: Waves, Nonlinearities and Nonlocalities - The Abel Symposium 2023. Abel Symposia, VOL. 18 ABEL, Springer Science and Business Media Deutschland GmbH, p. 93-109, Abel Symposium on Partial Differential Equations: Waves, Nonlinearities and Nonlocalities, 2023, Orkanger, Norvcge, 13/06/23. https://doi.org/10.1007/978-3-031-91282-5_5

Almost Sharp Rates of Convergence for the Average Cost and Displacement in the Optimal Matching Problem. / Goldman, Michael; Huesmann, Martin; Otto, Felix.
Partial Differential Equations: Waves, Nonlinearities and Nonlocalities - The Abel Symposium 2023. Ed. / Mats Ehrnström; Helge Holden; Espen R. Jakobsen. Springer Science and Business Media Deutschland GmbH, 2025. p. 93-109 (Abel Symposia; Vol 18 ABEL).

Résultats de recherche: Le chapitre dans un livre, un rapport, une anthologie ou une collection › Contribution à une conférence › Revue par des pairs

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N2 - 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.

AB - 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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Goldman M, Huesmann M, Otto F. Almost Sharp Rates of Convergence for the Average Cost and Displacement in the Optimal Matching Problem. Dans Ehrnström M, Holden H, Jakobsen ER, rédacteurs en chef, Partial Differential Equations: Waves, Nonlinearities and Nonlocalities - The Abel Symposium 2023. Springer Science and Business Media Deutschland GmbH. 2025. p. 93-109. (Abel Symposia). doi: 10.1007/978-3-031-91282-5_5