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GT CalVa F STRA
Lundi 15 mai 2017
Federico Stra (Scuola Normale Superiore di Pisa)
A PDE approach to a 2-dimensional matching problem
Abstract : In the seminar I present the result of a collaboration with Luigi Ambrosio and Dario Trevisan. We prove asymptotic results for 2-dimensional random matching problems. In particular, we obtain the leading term in the asymptotic expansion of the expected quadratic transportation cost for empirical measures of two samples of independent uniform random variables in the square. Our technique is based on a rigorous formulation of the challenging PDE ansatz by S. Caracciolo et al. (Phys. Rev. E, 90, 012118, 2014) that linearizes the Monge-Ampère equation.