A New Notion of Weak Transport Cost and Applications

Friday, May 1, 2015 - 10:15am - 11:05am
Keller 3-180
Cyril Roberto (Université Paris Ouest)
We introduce a new notion of (weak) transport cost on the Euclidean space that, with the help of the Kantorovich duality presented in the lecture by Paul-Marie Samson on Thursday, will give rise to some applications: (1) a new very short proof of a result by Strassen, (2) a characterization of those probablity measures satisfying the log-Sobolev inequality restricted to convex functions, and (3) a characterization of those probability measures on the line satisfying some Talagrand type transport-entropy inequality.

Based on two joint works with Nathael Gozlan, Paul-Marie Samson, Yan Shu and Prasad Tetali.
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