Abstract for the talk on 28.10.2016 (11:00 h)Arbeitsgemeinschaft ANGEWANDTE ANALYSIS
Yan Shu (Université Paris Ouest Nanterre)
On the optimal weak transfer plan
We study an optimal weak transport cost related to the notion of convex order between probability measures. On the real line, we show a link between Kantorovich duality and the permutation polytope by characterizing the transfer plan in two different ways. We prove that this weak transport cost is reached for a coupling that does not depend on the underlying cost function. As an application, we give a characterization for convex modified log sobolev inequality and a class of weak transport-entropy inequalities.
This talk contains results of a join work with N. Gozlan, C. Roberto, P-M. Samson and P. Tetali, and a join work of M. Strzelecki.