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New estimates on the matching problem

Luigi Ambrosio, Scola Normale Superiore, Pisa,Italy

Location:  HILL 705
Date & time: Friday, 10 November 2017 at 2:00PM - 3:00PM

23rd D'Atri Memorial Lectures

Abstract:  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 semi-group smoothing techniques and Dacorogna-Moser interpolation provide first rigorous results for this ansatz.

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

This talk is part of the D'Atri Memorial Lectures. Light refreshments at 1:30pm in Room 703.

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