[Estimations plus fines sur le problème de couplage]
Nous étudions le comportement asymptotique de l’espérance du coût du problème de couplage aléatoire dans une variété compacte de dimension , améliorant en de nombreux points les résultats de [AST18]. En particulier, nous simplifions la preuve originale et nous déterminons le coefficient dominant du développement asymptotique de l’espérance du coût du couplage aléatoire biparti dans une variété compacte de dimension . Nous précisons aussi l’estimation du terme d’erreur dans [Led18] pour le couplage semi-discret. Nous développons une estimation de contraction plus fine pour le flot de la chaleur sur des données aléatoires qui peut avoir un intérêt indépendant du reste de l’article.
We study the asymptotic behaviour of the expected cost of the random matching problem on a -dimensional compact manifold, improving in several aspects the results of [AST18]. 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 -dimensional closed manifold. We also sharpen the estimate of the error term given in [Led18] 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.
Accepté le :
Publié le :
DOI : 10.5802/jep.105
Keywords: Optimal transport, matching problem, heat semigroup
Mot clés : Transport optimal, problème de couplage, semi-groupe de la chaleur
Luigi Ambrosio 1 ; Federico Glaudo 2
CC-BY 4.0
@article{JEP_2019__6__737_0,
author = {Luigi Ambrosio and Federico Glaudo},
title = {Finer estimates on the~$2$-dimensional~matching~problem},
journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
pages = {737--765},
publisher = {\'Ecole polytechnique},
volume = {6},
year = {2019},
doi = {10.5802/jep.105},
zbl = {07114037},
language = {en},
url = {https://jep.centre-mersenne.org/articles/10.5802/jep.105/}
}
TY - JOUR AU - Luigi Ambrosio AU - Federico Glaudo TI - Finer estimates on the $2$-dimensional matching problem JO - Journal de l’École polytechnique — Mathématiques PY - 2019 SP - 737 EP - 765 VL - 6 PB - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.105/ DO - 10.5802/jep.105 LA - en ID - JEP_2019__6__737_0 ER -
%0 Journal Article %A Luigi Ambrosio %A Federico Glaudo %T Finer estimates on the $2$-dimensional matching problem %J Journal de l’École polytechnique — Mathématiques %D 2019 %P 737-765 %V 6 %I École polytechnique %U https://jep.centre-mersenne.org/articles/10.5802/jep.105/ %R 10.5802/jep.105 %G en %F JEP_2019__6__737_0
Luigi Ambrosio; Federico Glaudo. Finer estimates on the $2$-dimensional matching problem. Journal de l’École polytechnique — Mathématiques, Tome 6 (2019), pp. 737-765. doi : 10.5802/jep.105. https://jep.centre-mersenne.org/articles/10.5802/jep.105/
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