Subadditivity and optimal matching of unbounded samples
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913421774028800 |
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| author | Caglioti, Emanuele Goldman, Michael Pieroni, Francesca Trevisan, Dario |
| author_facet | Caglioti, Emanuele Goldman, Michael Pieroni, Francesca Trevisan, Dario |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_06352 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Subadditivity and optimal matching of unbounded samples Caglioti, Emanuele Goldman, Michael Pieroni, Francesca Trevisan, Dario Probability Mathematical Physics Functional Analysis Statistics Theory 60D05, 90C05, 39B62, 60F25, 49Q22 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. |
| title | Subadditivity and optimal matching of unbounded samples |
| topic | Probability Mathematical Physics Functional Analysis Statistics Theory 60D05, 90C05, 39B62, 60F25, 49Q22 |
| url | https://arxiv.org/abs/2407.06352 |