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On multiple covering of a circle with random arcs

Published online by Cambridge University Press:  14 July 2016

Lars Holst
Lars Holst*
Affiliation:
Uppsala University
*
∗Postal address: Department of Mathematics, Uppsala University. Thunbergsvägen 3, S–75238 Uppsala, Sweden.
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Abstract

On a circle of unit circumference arcs of length a are placed at random. Let Nα be equal to the necessary number of arcs to cover at least the length 1 − p, 0 ≦ p < 1, of the circumference at least m (≧1) times. In the present paper limit distributions of Nα are derived when α → 0. Some results for spacings are also obtained.

Keywords

COVERING A CIRCLESPACINGSUNIFORM DISTRIBUTIONLIMIT THEOREMS
Type
Short Communications
Information
Journal of Applied Probability , Volume 17 , Issue 1 , March 1980 , pp. 284 - 290
Copyright
Copyright © Applied Probability Trust 1980 

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