Online seminar: On the interactions between Statistics and Geometry

optimal transport
bipartite matching
occupation measure
slides
Author

Dario Trevisan

Published

November 8, 2024

I presented some recent developments on the Asymptotics for Random Quadratic Transportation Costs” at the online seminar On the interactions between Statistics and Geometry. Check their website for a recording of my talk but also many other ones!

During my presentation, I discussed some aspects of the transportation problem between random i.i.d. points and their common distribution, particularly focusing on cases governed by the squared Euclidean distance cost in dimensions greater than three. This topic has garnered significant interest in recent years, yet fine results concerning the limiting constants were limited to one or two dimensions or specific distributions. In a recent joint work with M. Huesmann and M. Goldman we expand these boundaries by settling the existence of a limit in any dimension for quadratic costs.

Slides are available here.

Boundary transport between a 400 pairs of i.i.d. simulated points on the unit square

In closing, I want to thank the organizers Victor-Emmanuel Brunel, Austin Stomme, Alexey Kroshnin, and Quentin Paris for their hard work in launching this series and for the opportunity to present my research!