dc.contributor.author | Holroyd, Alexander E. | |
dc.contributor.author | Lyons, Russell | |
dc.contributor.author | Soo, Terry | |
dc.date.accessioned | 2015-03-24T19:08:29Z | |
dc.date.available | 2015-03-24T19:08:29Z | |
dc.date.issued | 2011-11-02 | |
dc.identifier.citation | Holroyd, Alexander E.; Lyons, Russell; Soo, Terry. Poisson splitting by factors. Ann. Probab. 39 (2011), no. 5, 1938--1982. http://dx.doi.org/10.1214/11-AOP651. | en_US |
dc.identifier.uri | http://hdl.handle.net/1808/17202 | |
dc.description | This is the published version, also available here: http://dx.doi.org/10.1214/11-AOP651. | en_US |
dc.description.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. | en_US |
dc.publisher | Institute of Mathematical Statistics | en_US |
dc.subject | Poisson process | en_US |
dc.subject | stochastic domination | en_US |
dc.subject | factor map | en_US |
dc.subject | thinning | en_US |
dc.title | Poisson splitting by factors | en_US |
dc.type | Article | |
kusw.kuauthor | Soo, Terry | |
kusw.kudepartment | Mathematics | en_US |
dc.identifier.doi | 10.1214/11-AOP651 | |
kusw.oaversion | Scholarly/refereed, publisher version | |
kusw.oapolicy | This item meets KU Open Access policy criteria. | |
dc.rights.accessrights | openAccess | |