We study a multimarginal optimal transportation problem in one dimension. For a sym- metric, repulsive cost function, we show that, given a minimizing transport plan, its symmetrization is induced by a cyclical map, and that the symmetric optimal plan is unique. The class of costs that we consider includes, in particular, the Coulomb cost, whose optimal transport problem is strictly related to the strong interaction limit of Density Functional Theory. In this last setting, our result justifies some qualitative properties of the potentials observed in numerical experiments.

Multimarginal Optimal Transport Maps for 1-Dimensional Repulsive Costs / Colombo, M.; De Pascale, L.; Di Marino, S.. - In: CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES. - ISSN 0008-414X. - STAMPA. - 67:2(2018), pp. 350-368. [10.4153/CJM-2014-011-x]

Multimarginal Optimal Transport Maps for 1-Dimensional Repulsive Costs

DE PASCALE, LUIGI
;
2018

Abstract

We study a multimarginal optimal transportation problem in one dimension. For a sym- metric, repulsive cost function, we show that, given a minimizing transport plan, its symmetrization is induced by a cyclical map, and that the symmetric optimal plan is unique. The class of costs that we consider includes, in particular, the Coulomb cost, whose optimal transport problem is strictly related to the strong interaction limit of Density Functional Theory. In this last setting, our result justifies some qualitative properties of the potentials observed in numerical experiments.
2018
67
350
368
Colombo, M.; De Pascale, L.; Di Marino, S.
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1070980
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