Published Paper

Inserted: 8 aug 2022
Last Updated: 20 oct 2023

Journal: Probability Theory and Related Fields
Year: 2021
Doi: https://doi.org/10.1007/s00440-023-01225-5

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.