Transport Inequalities on Euclidean Spaces for Non-Euclidean Metrics

Sergey G. Bobkov; Michel Ledoux

doi:10.1007/s00041-020-09766-2

Transport Inequalities on Euclidean Spaces for Non-Euclidean Metrics

Sergey G. Bobkov
, Michel Ledoux

School of Mathematics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

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.

Original language	English (US)
Article number	60
Journal	Journal of Fourier Analysis and Applications
Volume	26
Issue number	4
DOIs	https://doi.org/10.1007/s00041-020-09766-2
State	Published - Aug 1 2020

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Publisher Copyright:
© 2020, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords

Fourier analytic inequalities
Transport distances
non-Euclidean metrics

Publisher link

10.1007/s00041-020-09766-2

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title = "Transport Inequalities on Euclidean Spaces for Non-Euclidean Metrics",

abstract = "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.",

keywords = "Fourier analytic inequalities, Transport distances, non-Euclidean metrics",

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AU - Ledoux, Michel

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N2 - 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.

AB - 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.

KW - Fourier analytic inequalities

KW - Transport distances

KW - non-Euclidean metrics

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UR - https://www.scopus.com/pages/publications/85087437921#tab=citedBy

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DO - 10.1007/s00041-020-09766-2

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AN - SCOPUS:85087437921

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JO - Journal of Fourier Analysis and Applications

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Transport Inequalities on Euclidean Spaces for Non-Euclidean Metrics

Abstract

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Keywords

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