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Random coverings of the circle by arcs with restricted endpoints
Published online by Cambridge University Press: 14 July 2016
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).
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- Copyright © Applied Probability Trust 1988
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