Article Dans Une Revue Annales de la Faculté des Sciences de Toulouse. Mathématiques. Année : 2026

Subadditivity and optimal matching of unbounded samples

Résumé

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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Dates et versions

hal-04639188 , version 1 (08-07-2024)
hal-04639188 , version 2 (08-01-2026)

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  • HAL Id : hal-04639188 , version 1

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Emanuele Caglioti, Michael Goldman, Francesca Pieroni, Dario Trevisan. Subadditivity and optimal matching of unbounded samples. Annales de la Faculté des Sciences de Toulouse. Mathématiques., In press. ⟨hal-04639188v1⟩
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