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A limit theorem for random coverings of a circle which do not quite cover

Published online by Cambridge University Press:  14 July 2016

Norman Kaplan
Norman Kaplan*
Affiliation:
University of California, Berkeley
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Abstract

We study the asymptotic behavior as α → 0 of the number of independent random arcs of length a needed to cover at least 1 − Kα (K ≧ 1) of a circle of unit circumference.

Keywords

RANDOM COVERINGS
Type
Short Communications
Information
Journal of Applied Probability , Volume 15 , Issue 2 , June 1978 , pp. 443 - 446
Copyright
Copyright © Applied Probability Trust 1978 

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References

[1] Flatto, L. (1973) A limit theorem for random coverings of a circle. Israel J. Maths 15, 167–184.Google Scholar
[2] Karlin, S. (1969) A First Course in Stochastic Processes. Academic Press, New York.Google Scholar