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arXiv · 2109.13590

There is no stationary cyclically monotone Poisson matching in 2d

Martin Huesmann·Francesco Mattesini·Felix Otto
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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.

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Martin Huesmann, Francesco Mattesini, Felix Otto. 2021-09-28. There is no stationary cyclically monotone Poisson matching in 2d. https://arxiv.org/abs/2109.13590

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