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arXiv · 2311.17687

There is no stationary $p$-cyclically monotone Poisson matching in 2D

Martin Huesmann·Francesco Mattesini·Felix Otto
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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 \cite[Theorem 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.

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Martin Huesmann, Francesco Mattesini, Felix Otto. 2023-11-29. There is no stationary $p$-cyclically monotone Poisson matching in 2D. https://arxiv.org/abs/2311.17687

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