A PDE approach to a 2-dimensional matching problem

被引:56
|
作者
Ambrosio, Luigi [1 ]
Stra, Federico [1 ]
Trevisan, Dario [2 ]
机构
[1] Scuola Normale Super Pisa, Pisa, Italy
[2] Univ Pisa, Pisa, Italy
关键词
Minimal matching; Optimal transport; Geometric probability; CURVATURE-DIMENSION CONDITION; TRANSPORTATION COST; CONVERGENCE;
D O I
10.1007/s00440-018-0837-x
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
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-Ampere equation.
引用
收藏
页码:433 / 477
页数:45
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