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February 2022 Applications of weak transport theory
J. Backhoff-Veraguas, G. Pammer
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Bernoulli 28(1): 370-394 (February 2022). DOI: 10.3150/21-BEJ1346

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.

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J. Backhoff-Veraguas. G. Pammer. "Applications of weak transport theory." Bernoulli 28 (1) 370 - 394, February 2022. https://doi.org/10.3150/21-BEJ1346

Information

Received: 1 August 2020; Revised: 1 March 2021; Published: February 2022
First available in Project Euclid: 10 November 2021

Digital Object Identifier: 10.3150/21-BEJ1346

Keywords: Brenier–Strassen theorem , cyclical monotonicity , Duality , linear transfers , optimal mechanism design , Schrödinger problem , semimartingale transport , weak transport problem

Rights: Copyright © 2022 ISI/BS

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Vol.28 • No. 1 • February 2022
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