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* Optimal transport in one dimension; Villani (73-78); Santambrogio (59-67) | * Optimal transport in one dimension; Villani (73-78); Santambrogio (59-67) | ||
* 1-Wasserstein metric, duality, and measures with unequal mass; [https://arxiv.org/pdf/1910.05105.pdf Piccoli, Rossi, and Tournus ''A Wasserstein norm for signed measures, with application to nonlocal transport equation with source term''] | * 1-Wasserstein metric, duality, and measures with unequal mass; [https://arxiv.org/pdf/1910.05105.pdf Piccoli, Rossi, and Tournus ''A Wasserstein norm for signed measures, with application to nonlocal transport equation with source term''] | ||
* Entropic optimal transport and the Shr\"dinger bridge problem [https://www.math.ucdavis.edu/~saito/data/acha.read.s19/leonard_survey-schroedinger-problem-optxport.pdf] | * Entropic optimal transport and the Shr\"dinger bridge problem [https://www.math.ucdavis.edu/~saito/data/acha.read.s19/leonard_survey-schroedinger-problem-optxport.pdf][https://www.math.columbia.edu/~mnutz/docs/EOT_lecture_notes.pdf] | ||
==The 2-Wasserstein Metric== | ==The 2-Wasserstein Metric== | ||
Revision as of 20:21, 20 January 2022
Below, you can find a list of new article ideas and suggested references. (Feel free to incorporate additional references! Please list all references you use at the bottom of your article.) If you choose to write about one of these ideas, remove it from the list below and create a new link on the main page.
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The Optimal Transport Problem
- Optimal transport in one dimension; Villani (73-78); Santambrogio (59-67)
- 1-Wasserstein metric, duality, and measures with unequal mass; Piccoli, Rossi, and Tournus A Wasserstein norm for signed measures, with application to nonlocal transport equation with source term
- Entropic optimal transport and the Shr\"dinger bridge problem [1][2]
The 2-Wasserstein Metric
- Displacement convexity; Santambrogio (249-251,271-276); Villani (150-154)
- Gradient flows in metric spaces, Santambrogio, 'OT for Applied Mathematicians' (285-290); Santambrogio, 'Euclidean, Metric, and Wasserstein GFs' (90-107; don't need to cover all topics, just what interests you)
Numerical Methods for Optimal Transport
- Computing OT via Benamou-Brenier; Santambrogio (220-225); Peyré, Cuturi (102-108)
- Wasserstein Barycenters; Santambrogio (215-218); Peyré, Cuturi (138-144)