An External Dual Charge Approach to the Multimarginal Optimal Transport with Coulomb Cost

Rodrigue Lelotte

doi:10.1051/cocv/2024017

An External Dual Charge Approach to the Multimarginal Optimal Transport with Coulomb Cost

Rodrigue Lelotte

Université Paris Dauphine

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

In this paper, we study the multimarginal optimal transport with Coulomb cost, also known in the physics literature as the Strictly-Correlated Electrons functional. We prove that the dual Kantorovich potential is an electrostatic potential induced by an external charge density, which we call the dual charge. We study its properties and use it to discretize the potential in one and three space dimensions.

langue originale	Anglais
Numéro d'article	56
journal	ESAIM - Control, Optimisation and Calculus of Variations
Volume	30
Les DOIs	https://doi.org/10.1051/cocv/2024017
état	Publié - 1 janv. 2024
Modification externe	Oui

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10.1051/cocv/2024017

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abstract = "In this paper, we study the multimarginal optimal transport with Coulomb cost, also known in the physics literature as the Strictly-Correlated Electrons functional. We prove that the dual Kantorovich potential is an electrostatic potential induced by an external charge density, which we call the dual charge. We study its properties and use it to discretize the potential in one and three space dimensions.",

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AB - In this paper, we study the multimarginal optimal transport with Coulomb cost, also known in the physics literature as the Strictly-Correlated Electrons functional. We prove that the dual Kantorovich potential is an electrostatic potential induced by an external charge density, which we call the dual charge. We study its properties and use it to discretize the potential in one and three space dimensions.

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KW - Strictly Correlated Electrons

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An External Dual Charge Approach to the Multimarginal Optimal Transport with Coulomb Cost

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