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Preprints, Working Papers, ... Year : 2024

Subadditivity and optimal matching of unbounded samples


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 $p\le d$. 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.
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hal-04639188 , version 1 (08-07-2024)


  • HAL Id : hal-04639188 , version 1


Emanuele Caglioti, Michael Goldman, Francesca Pieroni, Dario Trevisan. Subadditivity and optimal matching of unbounded samples. 2024. ⟨hal-04639188⟩
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