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Séminaire du LJLL - 05 07 2019 10h30 : L. Ambrosio
Luigi Ambrosio (Ecole Normale Supérieure de Pise)
Attention, horaire exceptionnel : 10h30 et non 14h00 !
New estimates on the matching problem
Résumé
The matching problem consists in finding the optimal coupling between a random distribution of N points in a d-dimensional domain and another (possibly random) distribution. There is a large literature on the asymptotic behaviour as N tends to infinity of the expectation of the minimum cost, and the results depend on the dimension d and of the choice of the cost in this random optimal transport problem. In a recent work, Caracciolo, Lucibello, Parisi and Sicuro proposed an ansatz for the expansion in N of the expectation. I will illustrate how a combination of semigroup smoothing techniques and of Dacorogna-Moser interpolation provide first rigorous results for this ansatz.
The talk will be based on joint works with Federico Glaudo, Federico Stra, Dario Trevisan.