Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5772296 | Journal of Functional Analysis | 2017 | 79 Pages |
Abstract
We introduce a general notion of transport cost that encompasses many costs used in the literature (including the classical one and weak transport costs introduced by Talagrand and Marton in the 90's), and prove a Kantorovich type duality theorem. As a by-product we obtain various applications in different directions: we give a short proof of a result by Strassen on the existence of a martingale with given marginals, we characterize the associated transport-entropy inequalities together with the log-Sobolev inequality restricted to convex/concave functions. We also provide explicit examples of discrete measures satisfying the weak transport-entropy inequalities derived here.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Nathael Gozlan, Cyril Roberto, Paul-Marie Samson, Prasad Tetali,