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 Caracciolo et al. (Phys Rev E 90:012118, 2014) that linearizes the Monge–Ampère equation.

A PDE approach to a 2-dimensional matching problem

Luigi Ambrosio;Federico Stra;
2018

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 Caracciolo et al. (Phys Rev E 90:012118, 2014) that linearizes the Monge–Ampère equation.
2018
Settore MAT/05 - Analisi Matematica
Geometric probability; Minimal matching; Optimal transport
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/81585
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