# Poisson Matching

@inproceedings{Holroyd2007PoissonM,
title={Poisson Matching},
author={A. Holroyd and R. Pemantle and Y. Peres and O. Schramm},
year={2007}
}
Suppose that red and blue points occur as independent homogeneous Poisson processes in Rd. We investigate translation-invariant schemes for perfectly matching the red points to the blue points. For any such scheme in dimensions d = 1, 2, the matching distance X from a typical point to its partner must have infinite d/2-th moment, while in dimensions d ≥ 3 there exist schemes where X has finite exponential moments. The Gale-Shapley stable marriage is one natural matching scheme, obtained by… Expand

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