Carlos A.C.C. Perello will give a talk on 04/01/2025.

We disprove the existence of a locally optimal, stationary and ergodic matching between two Poisson Point Processes in \mathbb{R}^2, which extends the literature on matchings between points sampled uniformly at random from a bounded domain to the plane, and connects this highly-geometric problem with (discrete) optimal transport.

The main tool used in this analysis is the so-called Harmonic approximation theorem introduced by Goldman, Huessmann and Otto, which quantitavely analyses the well-known fact that the Monge-Ampere equation near the Lebesgue measure linearises to be the Poisson equation. All work is based on (https://arxiv.org/abs/2109.13590).