Mathematics Colloquium

Tel Aviv University

Monday, May 29, 2017
Melamed Hall, Shenkar Physics
:: Sackler Distinguished Lecture in Mathematics ::
Luigi Ambrosio
Scuola Normale Superiore di Pisa
New estimates on the matching problem

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 the choice of 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 Dacorogna–Moser interpolation provide the first rigorous results for this ansatz.

Joint work with Federico Stra and Dario Trevisan, arXiv:1611.04960

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