preprint

Inserted: 30 nov 2023

Year: 2023

Abstract:

We show that for $p>1$ there is no $p$-cyclically monotone stationary matching of two independent Poisson processes in dimension $d=2$. The proof combines the $p$-harmonic approximation result from \citeTheorem 1.1{koch23} with local asymptotics for the two-dimensional matching problem. Moreover, we prove a.s. local upper bounds of the correct order in the case $p>1$, which, to the best of our knowledge, are not readily available in the current literature.