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.

中文翻译：

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具有有限排斥成本的边际

我们考虑具有排斥成本的多边际运输问题，其中边际都等于固定概率 $\unicode[STIX]{x1D70C}\in {\mathcal{P}}(\mathbb{R}^{d})$ . 我们证明，如果 $\unicode[STIX]{x1D70C}$ 的集中度小于 $1/N$ ，则该问题具有有限代价的解。结果是尖锐的，因为存在 $\unicode[STIX]{x1D70C}$ 的浓度为 $1/N$，其成本是无限的。