Geodesic
Marginals with Finite Repulsive Cost
Canadian journal of mathematics, Tome 72 (2020) no. 2, pp. 373-391

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DOI

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.
DOI : 10.4153/S0008414X18000664
Mots-clés : multi-marginal, optimal transport, repulsive cost 
Bindini, Ugo. Marginals with Finite Repulsive Cost. Canadian journal of mathematics, Tome 72 (2020) no. 2, pp. 373-391. doi: 10.4153/S0008414X18000664
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     title = {Marginals with {Finite} {Repulsive} {Cost}},
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     year = {2020},
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     doi = {10.4153/S0008414X18000664},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X18000664/}
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