Année 2021-2022

On recent progress on the optimal matching problem

by Michael Goldman

1013 (Université de Paris - Bâtiment Sophie Germain)


Université de Paris - Bâtiment Sophie Germain


The optimal matching problem is a classical random combinatorial problem which may be interpreted as an optimal transport problem between random measures. Recent years have seen a renewed interest for this problem   thanks to the PDE ansatz proposed in the physics literature by Caracciolo and al. and partially rigorously justified by Ambrosio-Stra-Trevisan. In this talk I will show how this ansatz combined with subadditivity may be used to give information both on the optimal cost and on the structure of the optimal transport map at various scales. This is based on joint works with L. Ambrosio, M. Huesmann, F. Otto and D. Trevisan.

Organized by

Maxime Laborde