Calculus of Variations and Geometric Measure Theory

U. Bindini

Marginals with finite repulsive cost

created by bindini on 07 Dec 2017
modified on 03 Aug 2021


Published Paper

Inserted: 7 dec 2017
Last Updated: 3 aug 2021

Journal: Canad. J. Math.
Volume: 72
Number: 2
Pages: 19
Year: 2020

ArXiv: 1702.06301 PDF


We consider a multimarginal transport problem with repulsive cost, where the marginals are all equal to a fixed probability $\rho \in \mathcal{P}(\mathbb{R}^d)$. We prove that, if the concentration of $\rho$ is less than $1/N$, then the problem has a solution of finite cost. The result is sharp, in the sense that there exists $\rho$ with concentration $1/N$ for which $C(\rho) = \infty$.

Keywords: Optimal transport, Repulsive potentials