Calculus of Variations and Geometric Measure Theory
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A PDE approach to a 2-dimensional matching problem

Federico Stra (Scuola Normale Superiore)

created by gelli on 16 Nov 2016

23 nov 2016 -- 17:00   [open in google calendar]

Sala Seminari Dipartimento di Matematica di Pisa

Abstract.

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.

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