A PDE approach to a 2-dimensional matching problem
Probability
2016-11-16 v1 Mathematical Physics
Analysis of PDEs
math.MP
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-Amp\`ere equation.
Cite
@article{arxiv.1611.04960,
title = {A PDE approach to a 2-dimensional matching problem},
author = {Luigi Ambrosio and Federico Stra and Dario Trevisan},
journal= {arXiv preprint arXiv:1611.04960},
year = {2016}
}