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A non-random limit for the volume covered k times

Published online by Cambridge University Press:  14 July 2016

A. J. Stam
A. J. Stam*
Affiliation:
Rijksuniversiteit Groningen
*
∗ Postal address: Mathematisch Instituut, Rijksuniversiteit te Groningen, Postbus 800, Groningen, The Netherlands.
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Abstract

Let n sets with volume ~ n -–1 be placed in Rm , independently and with the same distribution. As n →∞, the volume in V CRm , covered by exactly k of these sets under certain conditions converges to a non-random limit, which is the integral over V of a density that is of the type of a Poisson probability.

Keywords

RANDOM SETSVOLUME COVEREDCONVERGENCE IN MEAN

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 18 , Issue 1 , March 1981, pp. 148 - 156
Copyright
Copyright © Applied Probability Trust 

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