Finer estimates on the $2$-dimensional matching problem
| Autor: | Luigi Ambrosio, Federico Glaudo |
|---|---|
| Přispěvatelé: | Ambrosio, Luigi, Glaudo, Federico |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Matching (statistics)
Closed manifold Optimal matching General Mathematics Gaussian Upper and lower bounds law.invention symbols.namesake law Settore MAT/05 - Analisi Matematica Bipartite graph symbols Optimal Transport Matching problem Applied mathematics Asymptotic expansion Manifold (fluid mechanics) Mathematics |
| Popis: | We study the asymptotic behaviour of the expected cost of the random matching problem on a $2$-dimensional compact manifold, improving in several aspects the results of L. Ambrosio, F. Stra and D. Trevisan (A PDE approach to a 2-dimensional matching problem). In particular, we simplify the original proof (by treating at the same time upper and lower bounds) and we obtain the coefficient of the leading term of the asymptotic expansion of the expected cost for the random bipartite matching on a general 2-dimensional closed manifold. We also sharpen the estimate of the error term given by M. Ledoux (On optimal matching of Gaussian samples II) for the semi-discrete matching. As a technical tool, we develop a refined contractivity estimate for the heat flow on random data that might be of independent interest. |
| Databáze: | OpenAIRE |
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