There is no stationary $p$-cyclically monotone Poisson matching in 2D
Probability
2023-11-30 v1 Analysis of PDEs
Abstract
We show that for there is no -cyclically monotone stationary matching of two independent Poisson processes in dimension . The proof combines the -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 , which, to the best of our knowledge, are not readily available in the current literature.
Keywords
Cite
@article{arxiv.2311.17687,
title = {There is no stationary $p$-cyclically monotone Poisson matching in 2D},
author = {Martin Huesmann and Francesco Mattesini and Felix Otto},
journal= {arXiv preprint arXiv:2311.17687},
year = {2023}
}
Comments
Comments very welcome! arXiv admin note: text overlap with arXiv:2109.13590