Taylor expansions for the entropic optimal transport problem

par Flavien Léger (Mokaplan, Inria-Paris)

lundi 27 sept. 2021, 11:00 → 12:00 Europe/Paris

A305 (Université Paris-Dauphine)

We prove Taylor expansions of the entropic optimal transport problem with general cost as the temperature goes to zero. Our main contribution is a geometric Laplace expansion formula, where we express first-order terms as curvatures in the Kim-McCann geometry. We then obtain:

- first-order expansion of the potentials;

- second-order expansion of the transport value.

Joint work with Pierre Roussillon, François-Xavier Vialard and Gabriel Peyré.