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Marginals with Finite Repulsive Cost
Published online by Cambridge University Press: 07 May 2019
Abstract
We consider a multimarginal transport problem with repulsive cost, where the marginals are all equal to a fixed probability $\unicode[STIX]{x1D70C}\in {\mathcal{P}}(\mathbb{R}^{d})$. We prove that, if the concentration of $\unicode[STIX]{x1D70C}$ is less than $1/N$, then the problem has a solution of finite cost. The result is sharp, in the sense that there exists $\unicode[STIX]{x1D70C}$ with concentration $1/N$ for which the cost is infinite.
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- © Canadian Mathematical Society 2018