Session III.3 - Computational Optimal Transport
Wednesday, June 21, 17:30 ~ 18:00
Globally Lipschitz (non-optimal) transport maps
Max Fathi
Université Paris Cité, France - This email address is being protected from spambots. You need JavaScript enabled to view it.
Lipschitz transport maps allow to transfer functional and isoperimetric inequalities, such as logarithmic Sobolev inequalities, from one probability measure to another. For uniformly log-concave measures on Euclidean spaces, this can be done using quadratic optimal transport, thanks to Caffarelli's contraction theorem. In this talk, I will discuss a stochastic construction of Lipschitz transport maps due to Kim and Milman, and how it works in other settings, including some non-log-concave measures and Riemannian manifolds.
Joint work with Dan Mikulincer (MIT) and Yair Shenfeld (MIT).