There is no stationary cyclically monotone Poisson matching in 2d

Authors :: Huesmann, Martin
Mattesini, Francesco
Otto, Felix
Publication Year :: 2021
Publisher :: arXiv, 2021.
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.<br />Comment: Comments very welcome