OPTIMAL TRANSPORT FROM LEBESGUE TO POISSON

被引：24

作者：

Huesmann, Martin ^{[1
]}

Sturm, Karl-Theodor ^{[1
]}

机构：

[1] Univ Bonn, D-53115 Bonn, Germany

来源：

ANNALS OF PROBABILITY | 2013年 / 41卷 / 04期

关键词：

Optimal transportation; fair allocation; Laguerre tessellation; Poisson point process; METRIC-MEASURE-SPACES; GEOMETRY; EQUATIONS;

D O I：

10.1214/12-AOP814

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：

This paper is devoted to the study of couplings of the Lebesgue measure and the Poisson point process. We prove existence and uniqueness of an optimal coupling whenever the asymptotic mean transportation cost is finite. Moreover, we give precise conditions for the latter which demonstrate a sharp threshold at d = 2. The cost will be defined in terms of an arbitrary increasing function of the distance. The coupling will be realized by means of a transport map ("allocation map") which assigns to each Poisson point a set ("cell") of Lebesgue measure 1. In the case of quadratic costs, all these cells will be convex polytopes.

引用

页码：2426 / 2478

页数：53

共 31 条

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