Project Details
Projekt
Optimal matching and balancing transport
Subject Area
Mathematics
Term
since 2020
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 443976613
The optimal matching problem is one of the classical optimization problems in probability. By now, there is a good understanding of the macroscopic behaviour with some very detailed results, several challenging predictions, and open problems. The goal of this project is to develop a refined analysis of solutions to the optimal matching problem from a macroscopic scale down to a microscopic scale. Within this project, we concentrate on two main directions. On the one hand we are interested in quantitative convergence of the displacements of the optimal matching problem to Gaussian fields on mesoscopic scales. On the other hand we seek to obtain microscopic information by establishing (non-)existence of the thermodynamic limit. The main theoretical foundation for this project is a deterministic quantitative linearization result of the Monge-Ampère equation. In this project, we also aim to further push the deterministic regularity theory and test its applicability beyond the model case of iid uniform points.
DFG Programme
Priority Programmes
Subproject of
SPP 2265:
Random geometric systems
