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On the random coverage of the circle

Published online by Cambridge University Press:  14 July 2016

L. Holst  and
J. Hüsler
L. Holst*
Affiliation:
Uppsala University
J. Hüsler*
Affiliation:
University of Bern
*
∗Postal address: Department of Mathematics, Uppsala University, Thunbergsvägen 3, S-752 38 Uppsala, Sweden.
∗∗Postal address: Department of Mathematical Statistics, University of Bern, Sidlerstr. 5, CH-3012 Bern, Switzerland.
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Abstract

Place n arcs of equal length a uniformly at random on the circumference of a circle. We discuss the joint limit distributions of the number of gaps, the uncovered proportion of the circle and the lengths of the largest gap and of the smallest gap, depending on how a → 0 as n →∞.

We show that the results may be proved in a unified and simple way by using a result of Le Cam.

Keywords

JOINT LIMIT THEOREMSCOVERING A CIRCLESPACINGSUNIFORM DISTRIBUTION
Type
Research Papers
Information
Journal of Applied Probability , Volume 21 , Issue 3 , September 1984 , pp. 558 - 566
Copyright
Copyright © Applied Probability Trust 1984 

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