# Weak monotone rearrangement on the line

arXiv: https://arxiv.org/abs/1902.05763 · HTML: https://mlsanity.com/paper/1902.05763/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Feb 2019.

## Built on by (most cited first, 1 of 1)

- [A novel notion of barycenter for probability distributions based on optimal weak mass transport](https://mlsanity.com/paper/2102.13380/) (2021)

## Abstract (arXiv)

Weak optimal transport has been recently introduced by Gozlan et al. The original motivation stems from the theory of geometric inequalities; further applications concern numerics of martingale optimal transport and stability in mathematical finance. In this note we provide a complete geometric characterization of the 'weak' version of the classical monotone rearrangement between measures on the real line, complementing earlier results of Alfonsi, Corbetta, and Jourdain.