Abstract: The optimal matching problem is one of the classical random optimization problems. While the asymptotic behavior of the expected cost is well understood only little is known for the asymptotic behavior of the optimal couplings - the solutions to the optimal matching problem. In this talk we show that at all mesoscopic scales the displacement under the optimal coupling converges in suitable Sobolev spaces to a Gaussian field which can be identified as the curl-free part of a vector Gaussian free field. Based on joint work with Michael Goldman.

Date and time: Monday December 13, 17:30-18:30 (Rome time zone)

Zoom link:  https://us02web.zoom.us/j/8342220461

This is a talk of the (PMS)^2: Pavia-Milano Seminar series on Probability and Mathematical Statistics organized jointly by the universities Milano-Bicocca, Pavia, Milano-Politecnico and Milano-Statale. For more information see the dedicated webpage:
https://paviamilanoseminars.wordpress.com/

Participation is free and welcome!

Best regards
The organizers (Mario Maurelli, Carlo Orrieri, Maurizia Rossi, Margherita Zanella)