Article revision ideas

Below, you can find a list of revision ideas for articles. If you choose to write about one of these ideas, remove it from the list below and email me.

Please do not revise your own article unless you check with me first.

Want to revise an article that's not listed here? Email me!

List of Articles

Monge Problem

Kantorovich Problem

Optimal Transport in One Dimension

Kantorovich Dual Problem (for general costs)

• This article should be merged with article on the Kantorovich Dual Problem for c= d^2
• Add a discussion on the dual problem for c=d.

Discrete Optimal Transport

• Revision can begin on February 26

Fenchel-Rockafellar and Linear Programming

Optimal Transport and Ricci curvature

• Revision can begin on February 26
• Add a new section to the article discussing the relationship between Ricci curvature and convexity of the entropy. You should link to the existing wiki article on Geodesics and generalized geodesics.

Martingale optimal transport and mathematical finance

• Introduce some background material to explain the notation of what it means to be the expectation with respect to a filtration.
• Give intuition behind item (ii) in teh definition of an equivalent martingale measure
• Provide more intuition/background behind Problem 1 and 2. For example in Problem 2, what does it mean to be a martingale under Q? Why is that a natural requirement in this context?

Isoperimetric inequality and OMT

• Add sections describing recent work on *quantitative* isoperimetric inequalities, [1], [2]