POSTPONED: Dario Trevisan (Università di Pisa)
28 February 2020 @ 12:00 - 13:00
“The law of the optimal map in random Euclidean matching problems”
Random bipartite Euclidean matching problems can be seen as specific instances of optimal transport problems involving two random empirical measures, with a cost given by the Euclidean distance between pairs of sampled points. A heuristic approach, exploiting this connection and using a non-rigorous “linearization” of the problem, has been proposed in the physics literature (by Caracciolo et al. in 2014) strongly supported by numerical simulations. From a mathematical point of view, despite some partial success in the two dimensional case, many conjectures concerning asymptotics of matching/transportation costs and laws of optimal matchings/couplings remain open for a wide range of costs and geometries, especially in higher dimensional domains. Aim of this talk will be to review their current status, focusing on some recent results providing, in the two dimensional case, precise estimates on the distance between the optimal matching map and its “linearized” approximation (based on joint work with L. Ambrosio and F. Glaudo).