2024/07/08 by Emanuele Caglioti, Michaël Goldman, Caglioti, Emanuele +5
Mathematics · #advanced mathematical theories #Functional Equations Stability Results
paper · pdf · doi:10.48550/arxiv.2407.06352
We obtain new bounds for the optimal matching cost for empirical measures with unbounded support. For a large class of radially symmetric and rapidly decaying probability laws, we prove for the first time the asymptotic rate of convergence for the whole range of power exponents p and dimensions d. Moreover we identify the exact prefactor when p≤ d. We cover in particular the Gaussian case, going far beyond the currently known bounds. Our proof technique is based on approximate sub- and super-additivity bounds along a geometric decomposition adapted to some features the density, such as its radial symmetry and its decay at infinity.