On a mixture of Brenier and Strassen Theorems
By Nathael Gozlan, Nicolas Juillet. Proceedings of the London Mathematical Society, 2018
66 citations recorded by the source corpus.
We give a characterization of optimal transport plans for a variant of the usual quadratic transport cost introduced in Gozlan, Roberto, Samson and Tetali (J. Funct. Anal. 273 (2017) 3327–3405). Optimal plans are composition of a deterministic transport given by the gradient of a continuously differentiable convex function followed by a martingale coupling. We also establish some connections with Caffarelli's contraction theorem (Caffarelli, Comm. Math. Phys. 214 (2000) 547–563).
Subfields: Algebra and Number Theory, Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/2baa9b002711d3c6f30900cc61977fccfb09ba0b
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
- Mathias Beiglbock
- Sigrid Kallblad
- Julio Backhoff-Veraguas
- Mathias Beiglboeck
- Martin Huesmann
- Julio D. Backhoff Veraguas
- Gudmund Pammer
In Applied Mathematics
- Mathias Beiglbock
- Julio Backhoff-Veraguas
- Martin Huesmann
- Gudmund Pammer
- Sigrid Kallblad
- Julio D. Backhoff Veraguas
- Mathias Beiglboeck
- Daniel Bartl
Citations in the corpus
- Stability of martingale optimal transport and weak optimal transport (2019, unknown): “We also refer to [25, 21] for some unexpected applications of weak transport problems in analysis and probability.”
- Applications of weak transport theory (2020, unknown): “) • The Brenier–Strassen Theorem of Gozlan and Juillet [32] yields that 1-Lipschitz maps that are gradients to convex functions are the optimizers of transport problems with barycentric costs.”
- Existence, duality, and cyclical monotonicity for weak transport costs (2018, methodology): “In an updated version of [23], Gozlan and Juillet have also removed the compactness assumption in Theorem 1.”
- Martingale Benamou–Brenier: A probabilistic perspective (2017, methodology): “. Of course there are versions of the results in this section for general n-tuples instead of pairs. Since we only use the version with pairs we did not state the result in its most general form (cf. [27, 5]). 5. Pending proofs 5.1. Proof of Theorems 1.10 and 3.14. Proof of Theorem 1.10. Let A : R d”