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Random coverings of the circle by arcs with restricted endpoints

Published online by Cambridge University Press:  14 July 2016

Svante Janson
Svante Janson*
Affiliation:
Uppsala University
*
∗ Postal address: Department of Mathematics, Uppsala University, Thunbergsvägen 3, S-752 38 Uppsala, Sweden.
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Abstract

A circle is covered by random arcs with a given length a and endpoints chosen (independently and uniformly) among m equispaced points on the circle. The asymptotic distribution as a → 0 and m → ∞of the number of arcs required for complete coverage is given. The result connects earlier results for the cases ma = 1 (a discrete problem) and m = ∞ (the continuous limiting case).

Keywords

COUPON COLLECTION
Type
Short Communications
Information
Journal of Applied Probability , Volume 25 , Issue 1 , March 1988 , pp. 215 - 219
Copyright
Copyright © Applied Probability Trust 1988 

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References

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