Asymptotics of the Kantorovich Potential for the Optimal Transport with Coulomb Cost

TL;DR

This paper proves a conjecture about the long-range behavior of the Kantorovich potential in multimarginal optimal transport problems with Coulomb and Riesz costs, advancing theoretical understanding of these mathematical models.

Contribution

It establishes the asymptotic behavior at infinity of the Kantorovich potential for specific optimal transport problems, confirming a previously conjectured property.

Findings

Confirmed the conjecture on asymptotic behavior at infinity

Provided rigorous mathematical proof for Coulomb and Riesz costs

Enhanced theoretical understanding of multimarginal optimal transport

Abstract

We prove a conjecture regarding the asymptotic behavior at infinity of the Kantorovich potential for the Multimarginal Optimal Transport with Coulomb and Riesz costs.