TU Dortmund, Raum M611

The optimal matching problem is one of the classical random optimization problems. The macroscopic behaviour is well understood since the work of Ajtai, Komlos, Tusnady, Talagrand and others in the 80s and early 90s. A few years ago, Caracciolo et al. proposed a new ansatz, based on a linearisation of the Monge-Ampere equation to the Poisson equation, to get refined estimates for this problem. I will show how one can justify this approach in a quantitative way leading to a large scale regularity theory for the optimal transport problem. This in turn can then be used to get new information on the matching problem, like convergence to a Gaussian field which we will shortly discuss at the end of the talk.

Martin Huesmann

Münster