SISSA Mathematical Colloquia

[Emanuele Tuillier Illingworth]

*SISSA Mathematical Colloquia*

https://www.math.sissa.it/content/mathematical-colloquia-2016-2017

Prof. Luigi Ambrosio
Institution: SNS, Pisa
Location: A-128
Schedule: Monday, April 3, 2017 -16:00 to 17:00

/Title: New estimates on the matching problem/
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/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, with 
challenging open problems. 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 first rigorous 
results for this ansatz. Joint work with Federico Stra and Dario 
Trevisan, ArXiv:1611.04960/