Calculus of Variations and Geometric Measure Theory

M. Huesmann - F. Mattesini - F. Otto

There is no stationary cyclically monotone Poisson matching in 2d

created by mattesini on 08 Aug 2022

[BibTeX]

preprint

Inserted: 8 aug 2022

Year: 2021

ArXiv: 2109.13590 PDF

Abstract:

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 \cite{GHO} with local asymptotics for the two-dimensional matching problem for which we give a new self-contained proof using martingale arguments.