Applications of weak transport theory

J. Backhoff-Veraguas; G. Pammer

doi:10.3150/21-bej1346

Applications of weak transport theory

J. Backhoff-Veraguas, G. Pammer

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

Abstract

Motivated by applications to geometric inequalities, Gozlan, Roberto, Samson, and Tetali (J. Funct. Anal. 273 (2017) 3327–3405) introduced a transport problem for ‘weak’ cost functionals. Basic results of optimal transport theory can be extended to this setup in remarkable generality. In this article, we collect several problems from different areas that can be recast in the framework of weak transport theory, namely: the Schrödinger problem, the Brenier–Strassen theorem, optimal mechanism design, linear transfers, semimartingale transport. Our viewpoint yields a unified approach and often allows to strengthen the original results.

Original language	English
Pages (from-to)	370 - 394
Journal	Bernoulli
Volume	28
Issue number	1
DOIs	https://doi.org/10.3150/21-bej1346
Publication status	Published - 1 Feb 2022
Externally published	Yes

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abstract = "Motivated by applications to geometric inequalities, Gozlan, Roberto, Samson, and Tetali (J. Funct. Anal. 273 (2017) 3327–3405) introduced a transport problem for {\textquoteleft}weak{\textquoteright} cost functionals. Basic results of optimal transport theory can be extended to this setup in remarkable generality. In this article, we collect several problems from different areas that can be recast in the framework of weak transport theory, namely: the Schr{\"o}dinger problem, the Brenier–Strassen theorem, optimal mechanism design, linear transfers, semimartingale transport. Our viewpoint yields a unified approach and often allows to strengthen the original results.",

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Applications of weak transport theory

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