Abstract
We show that for there is no p-cyclically monotone stationary matching of two independent Poisson processes in dimension . The proof combines the p-harmonic approximation result from [15, Theorem 1.1] with local asymptotics for the two-dimensional matching problem. Moreover, we prove a.s. local upper bounds of the correct order in the case , which, to the best of our knowledge, are not readily available in the current literature.
Funding Statement
All authors are supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through the SPP 2265 Random Geometric Systems. MH and FM have been funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC 2044−390685587, Mathematics Münster: Dynamics–Geometry–Structure. FM has been funded by the Max Planck Institute for Mathematics in the Sciences.
Citation
Martin Huesmann. Francesco Mattesini. Felix Otto. "There is no stationary p-cyclically monotone Poisson matching in 2d." Electron. J. Probab. 29 1 - 20, 2024. https://doi.org/10.1214/24-EJP1171
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