On the optimal weak transfer plan

  • Yan Shu (Université Paris Ouest Nanterre)
A3 01 (Sophus-Lie room)


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.

Katja Heid

MPI for Mathematics in the Sciences Contact via Mail

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