There is no stationary cyclically monotone Poisson matching in 2d

被引：1
作者：
Huesmann, Martin [1 ]
Mattesini, Francesco [1 ,2 ]
Otto, Felix [2 ]
机构：
[1] Univ Munster, Inst Math Stochast, Orleans Ring 10, D-48149 Munster, Germany
[2] Max Planck Inst Math Nat Wissensch, Inselstr 22, D-04103 Leipzig, Germany
来源：
PROBABILITY THEORY AND RELATED FIELDS | 2023年 / 187卷 / 3-4期
关键词：
OPTIMAL TRANSPORT; ALLOCATION;
D O I：
10.1007/s00440-023-01225-5
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 show that there is no cyclically monotone stationary matching of two independent Poisson processes in dimension d = 2. The proof combines the harmonic approximation result from Goldman et al. (Commun. Pure Appl. Math. 74:2483-2560, 2021) with local asymptotics for the two-dimensional matching problem for which we give a new self-contained proof using martingale arguments.
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收藏
页码：629 / 656
页数：28
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