# Poisson splitting by factors

@article{Holroyd2011PoissonSB, title={Poisson splitting by factors}, author={Alexander E. Holroyd and Russell Lyons and Terry Soo}, journal={Annals of Probability}, year={2011}, volume={39}, pages={1938-1982} }

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… Expand

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