Intrinsic Sparsity of Kantorovich solutions

Let $X,Y$ be two finite sets of points having $\#X = m$ and $\#Y = n$ points with $\mu = (1/m)(\delta _{x_1} + \dots + \delta _{x_m})$ and $\nu = (1/n) (\delta _{y_1} + \dots + \delta _{y_n})$ being the associated uniform probability measures. A result of Birkhoff implies that if $m = n$, then the K...

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Bibliographic Details
Main Authors: Hosseini, Bamdad, Steinerberger, Stefan
Format: Article
Language:English
Published: Académie des sciences 2022-10-01
Series:Comptes Rendus. Mathématique
Online Access:https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.392/