The infinite dimensional Gaussian random matching problem - Dario Trevisan (Università di Pisa)

Abstract: The random matching problem consists of estimating the expected value of a transportation cost between the (random) empirical measure of independent identically distributed random variables, and their the common law, finding in particular asymptotic rates when the number of variables becomes large. Using a random PDE approach, M. Ledoux recently provided upper and lower bounds for the Wasserstein-Kantorovich cost in the case of standard Gaussian random variables, in any (but finite) dimension. In this seminar we will illustrate how a similar technique leads to some results in the infinite dimensional Gaussian setting, with applications e.g. the problem of matching samples of Brownian paths to the Wiener measure.