There is no stationary cyclically monotone Poisson matching in 2d

• 成果类型: Article
• 署名作者: Huesmann, Martin; Mattesini, Francesco; Otto, Felix
• 署名单位: University of Munster; Max Planck Society
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-023-01225-5
• 发表日期: 2023
• 页码: 629-656
• 关键词: optimal transport; allocation

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.