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Marginals with Finite Repulsive Cost
- Part of
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- Journal:
- Canadian Journal of Mathematics / Volume 72 / Issue 2 / April 2020
- Published online by Cambridge University Press:
- 07 May 2019, pp. 373-391
- Print publication:
- April 2020
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- Article
- Export citation
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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.
