Deterministic thinning of finite Poisson processes
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- by Omer Angel, Alexander E. Holroyd and Terry Soo PDF
- Proc. Amer. Math. Soc. 139 (2011), 707-720 Request permission
Abstract:
Let $\Pi$ and $\Gamma$ be homogeneous Poisson point processes on a fixed set of finite volume. We prove a necessary and sufficient condition on the two intensities for the existence of a coupling of $\Pi$ and $\Gamma$ such that $\Gamma$ is a deterministic function of $\Pi$, and all points of $\Gamma$ are points of $\Pi$. The condition exhibits a surprising lack of monotonicity. However, in the limit of large intensities, the coupling exists if and only if the expected number of points is at least one greater in $\Pi$ than in $\Gamma$.References
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Additional Information
- Omer Angel
- Affiliation: Department of Mathematics, University of British Columbia, 121–1984 Mathematics Road, Vancouver, BC V6T 1Z2, Canada
- MR Author ID: 667585
- Email: angel@math.ubc.ca
- Alexander E. Holroyd
- Affiliation: Microsoft Research, 1 Microsoft Way, Redmond, Washington 98052
- MR Author ID: 635612
- Email: holroyd@math.ubc.ca
- Terry Soo
- Affiliation: Department of Mathematics, University of British Columbia, 121–1984 Mathematics Road, Vancouver, BC V6T 1Z2, Canada
- MR Author ID: 888642
- Email: tsoo@math.ubc.ca
- Received by editor(s): December 2, 2009
- Received by editor(s) in revised form: December 4, 2009, and April 12, 2010
- Published electronically: August 19, 2010
- Additional Notes: Funded in part by Microsoft Research (AEH) and NSERC (all authors)
- Communicated by: Edward C. Waymire
- © Copyright 2010 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 139 (2011), 707-720
- MSC (2010): Primary 60G55
- DOI: https://doi.org/10.1090/S0002-9939-2010-10535-X
- MathSciNet review: 2736350