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1. There is no stationary cyclically monotone Poisson matching in 2d

Author

Huesmann, Martin, Mattesini, Francesco, and Otto, Felix

Subjects
Mathematics - Analysis of PDEs, Probability (math.PR), FOS: Mathematics, Mathematics - Probability, Analysis of PDEs (math.AP)
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., Comment: Comments very welcome

Published
2021
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