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Limit laws for the diameter of a random point set

Part of: Geometric probability and stochastic geometry Limit theorems

Published online by Cambridge University Press:  19 February 2016

Martin J. B. Appel ,
Christopher A. Najim  and
Ralph P. Russo
Martin J. B. Appel*
Affiliation:
MGIC
Christopher A. Najim*
Affiliation:
University of Iowa
Ralph P. Russo*
Affiliation:
University of Iowa
*
∗ Postal address: Capital Markets Operations, MGIC, 270 E. Kilbourn Ave, Milwaukee, WI 53202, USA.
∗∗ Postal address: Department of Statistics and Actuarial Science, University of Iowa, Iowa City, IA 52242, USA.
∗∗ Postal address: Department of Statistics and Actuarial Science, University of Iowa, Iowa City, IA 52242, USA.
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Abstract

Let U1,U2,… be a sequence of i.i.d. random vectors distributed uniformly in a compact plane region A of unit area. Sufficient conditions on the geometry of A are provided under which the Euclidean diameter Dn of the first n of the points converges weakly upon suitable rescaling.

Keywords

Maximum distancediameterextreme value distributiongeometric probability

MSC classification

Primary: 60F05: Central limit and other weak theorems
Secondary: 60D05: Geometric probability and stochastic geometry
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 34 , Issue 1 , March 2002 , pp. 1 - 10
Copyright
Copyright © Applied Probability Trust 2002 

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References

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