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Convex hulls of selected subsets of a Poisson process

Part of: General convexity Geometric probability and stochastic geometry Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Paul Blackwell
Paul Blackwell*
Affiliation:
University of Sheffield
*
∗ Postal address: Department of Probability and Statistics, University of Sheffield, Sheffield S3 7RH, UK.
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Abstract

This paper considers sets of points from a Poisson process in the plane, chosen to be close together, and their properties. In particular, the perimeter of the convex hull of such a point set is investigated. A number of different models for the selection of such points are considered, including a simple nearest-neighbour model. Extensions to marked processes and applications to modelling animal territories are discussed.

Keywords

POINT PROCESSESMARKED POINT PROCESSESANIMAL TERRITORIES

MSC classification

Primary: 60G55: Point processes
Secondary: 60D05: Geometric probability and stochastic geometry 52A22: Random convex sets and integral geometry
Type
Research Papers
Information
Journal of Applied Probability , Volume 29 , Issue 4 , December 1992 , pp. 814 - 824
Copyright
Copyright © Applied Probability Trust 1992 

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