Poisson Thickening

Details Poisson Thickening Poisson Thickening

2009-11-28

arxiv.org/abs/0911.5377v2

Mathematics

Probability

12 pages. Revised version with improved exposition and text.

Scientific paper

Let X be a Poisson point process of intensity lambda on the real line. A thickening of it is a (deterministic) measurable function f such that the union of X and f(X) is a Poisson point process of intensity lambda' where lambda'>lambda. An equivariant thickening is a thickening which commutes with all shifts of the line. We show that a thickening exists but an equivariant thickening does not. We prove similar results for thickenings which commute only with integer shifts and in the discrete and multi-dimensional settings. This answers 3 questions of Holroyd, Lyons and Soo.

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