Deterministic thinning of finite Poisson processes

Authors:
Omer Angel, Alexander E. Holroyd and Terry Soo

Journal:
Proc. Amer. Math. Soc. **139** (2011), 707-720

MSC (2010):
Primary 60G55

DOI:
https://doi.org/10.1090/S0002-9939-2010-10535-X

Published electronically:
August 19, 2010

MathSciNet review:
2736350

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Abstract | References | Similar Articles | Additional Information

Abstract: Let and 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 and such that is a deterministic function of , and all points of are points of . 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 than in .

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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

Email:
angel@math.ubc.ca

**Alexander E. Holroyd**

Affiliation:
Microsoft Research, 1 Microsoft Way, Redmond, Washington 98052

Email:
holroyd@math.ubc.ca

**Terry Soo**

Affiliation:
Department of Mathematics, University of British Columbia, 121–1984 Mathematics Road, Vancouver, BC V6T 1Z2, Canada

Email:
tsoo@math.ubc.ca

DOI:
https://doi.org/10.1090/S0002-9939-2010-10535-X

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

Article copyright:
© Copyright 2010
American Mathematical Society