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Coverage of the whole space

Part of: Geometric probability and stochastic geometry Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Ilya Molchanov  and
Vadim Scherbakov
Ilya Molchanov*
Affiliation:
University of Berne
Vadim Scherbakov*
Affiliation:
University of Glasgow
*
∗ Postal address: University of Berne, Department of Mathematical Statistics and Actuarial Science, Sidlerstrasse 5, CH-3012 Berne, Switzerland. Email address: ilya@stat.unibe.ch
∗∗ Postal address: University of Glasgow, Department of Statistics, Glasgow G12 8QW, UK.
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Abstract

Consider an inhomogeneous germ-grain model with spherical grains whose radii depend on their positions through a rate function, possibly perturbed by a random noise. We find the critical rate function that separates the cases when the germ-grain model covers the whole space with a positive probability and when the total coverage occurs with probability zero.

Keywords

Boolean modelcoveragegerm-grain model

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 60G55: Point processes
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 35 , Issue 4 , December 2003 , pp. 898 - 912
Copyright
Copyright © Applied Probability Trust 2003 

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