Poisson Matching
| dc.creator | Holroyd, Alexander E. | |
| dc.creator | Pemantle, Robin | |
| dc.creator | Peres, Yuval | |
| dc.creator | Schramm, Oded | |
| dc.date | 2007-12-12 | |
| dc.date | 2008-03-15 | |
| dc.date.accessioned | 2026-07-07T09:26:41Z | |
| dc.date.available | 2026-07-07T09:26:41Z | |
| dc.description | Suppose that red and blue points occur as independent homogeneous Poisson processes in R^d. 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 iteratively matching mutually closest pairs. A principal result of this paper is a power law upper bound on the matching distance X for this scheme. A power law lower bound holds also. In particular, stable marriage is close to optimal (in tail behavior) in d=1, but far from optimal in d>=3. For the problem of matching Poisson points of a single color to each other, in d=1 there exist schemes where X has finite exponential moments, but if we insist that the matching is a deterministic factor of the point process then X must have infinite mean. | |
| dc.description | 37 pages; to appear in Annales de l'institut Henri Poincare (B) | |
| dc.identifier | https://arxiv.org/abs/0712.1867 | |
| dc.identifier | http://arxiv.org/abs/0712.1867 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/156838 | |
| dc.subject | Probability | |
| dc.subject | 60D05; 60G55; 05C70 | |
| dc.title | Poisson Matching | |
| dc.type | text |