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

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	56
Journal	ESAIM - Control, Optimisation and Calculus of Variations
Volume	30
DOIs	https://doi.org/10.1051/cocv/2024017
Publication status	Published - 1 Jan 2024
Externally published	Yes

Keywords

Multimarginal Optimal Transport
Strictly Correlated Electrons

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10.1051/cocv/2024017

Cite this

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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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N2 - 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.

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.

KW - Multimarginal Optimal Transport

KW - Strictly Correlated Electrons

UR - https://www.scopus.com/pages/publications/85201240233

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DO - 10.1051/cocv/2024017

M3 - Article

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JO - ESAIM - Control, Optimisation and Calculus of Variations

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M1 - 56

ER -

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

Abstract

Keywords

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