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Poisson matching

Alexander E. HolroydRobin PemantleYuval PeresOded Schramm — 2009

Annales de l'I.H.P. Probabilités et statistiques

Suppose that red and blue points occur as independent homogeneous Poisson processes in ℝ. We investigate translation-invariant schemes for perfectly matching the red points to the blue points. For any such scheme in dimensions =1, 2, the matching distance from a typical point to its partner must have infinite /2th moment, while in dimensions ≥3 there exist schemes where has finite exponential moments. The Gale–Shapley stable marriage is one natural matching scheme, obtained by iteratively matching...

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