A PDE approach to a 2-dimensional matching problem

2016/11/15 by Ambrosio, Luigi, Stra, Federico, Trevisan, Dario · 7 citations
#60D05 (Primary) 49J55 #60H15 (Secondary) #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.1611.04960

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, \bf 90 012118, 2014) that "linearise" the Monge-Ampère equation.

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• Gap metrics for stationary point processes and quantitative convexity of the free energy
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