We explore upper bounds on Kantorovich transport distances between probability measures on the Euclidean spaces in terms of their Fourier-Stieltjes transforms, with focus on non-Euclidean metrics. The results are illustrated on empirical measures in the optimal matching problem on the real line.
Bibliographical noteFunding Information:
Research was partially supported by the Simons Foundation and NSF Grant DMS-1855575.
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- Fourier analytic inequalities
- Transport distances
- non-Euclidean metrics