Continuity Of Multimarginal Optimal Transport With Repulsive Cost

Maria Colombo, Federico Stra
2019
Article

Résumé

We provide sharp conditions for the finiteness and the continuity of multimarginal optimal transport with repulsive cost, expressed in terms of a suitable concentration property of the measure. To achieve this result, we analyze the Kantorovich potentials of the optimal plans, and we estimate the distance of any optimal plan from the regions where the cost is infinite.

Source officielle

https://infoscience.epfl.ch/record/270482?ln=fr

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We construct a measure on the thick points of a Brownian loop soup in a bounded domain D

D

of the plane with given intensity theta>0

\theta >0

, which is formally obtained by exponentiating the square root of its occupation field. The measure is construct ...

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Continuity Of Multimarginal Optimal Transport With Repulsive Cost

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