Holroyd, AE;
Lyons, R;
Soo, T;
(2011)
Poisson splitting by factors.
Annals of Probability
, 39
(5)
pp. 1938-1982.
10.1214/11-AOP651.
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Abstract
Given a homogeneous Poisson process on ℝd with intensity λ, we prove that it is possible to partition the points into two sets, as a deterministic function of the process, and in an isometry-equivariant way, so that each set of points forms a homogeneous Poisson process, with any given pair of intensities summing to λ. In particular, this answers a question of Ball [Electron. Commun. Probab. 10 (2005) 60–69], who proved that in d = 1, the Poisson points may be similarly partitioned (via a translation-equivariant function) so that one set forms a Poisson process of lower intensity, and asked whether the same is possible for all d. We do not know whether it is possible similarly to add points (again chosen as a deterministic function of a Poisson process) to obtain a Poisson process of higher intensity, but we prove that this is not possible under an additional finitariness condition.
| Type: | Article |
|---|---|
| Title: | Poisson splitting by factors |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1214/11-AOP651 |
| Publisher version: | https://doi.org/10.1214/11-AOP651 |
| Language: | English |
| Additional information: | This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10089089 |
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