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# Extremal Properties of Functionals in W_2 Space

ФИО студента: Plakhov Mikhail

Руководитель:

Кампус/факультет: Faculty of Mathematics

Программа: Mathematics (Bachelor)

Год защиты: 2020

In this paper we study a new approach to the proof of the fact that the infimum of Kantorovich distance on the space of all measures dominated by $\nu$ is reached, and that it is unique. This approach, which was first introduced by (Alfonsi et al. 2019), allows us to generalize the results of (N. Gozlan et al. 2017) for a wider set of Kantorovich distances (namely, $W_\rho(\mu, \nu), \rho &gt; 1$). We then study a new result, which explicitly describes the optimal transport map in the case of one-dimensional space.

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