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Random covering of the circle: the size of the connected components
Published online by Cambridge University Press: 01 July 2016
Abstract
Consider a circle of circumference 1. Throw n points at random onto this circle and append to each of these points a clockwise arc of length s. The resulting random set is a union of a random number of connected components, each with specific size. Using tools designed by Steutel, we compute the joint distribution of the lengths of the connected components. Asymptotic results are presented when n goes to ∞ and s to 0 jointly according to different regimes.
MSC classification
- Type
- Stochastic Geometry and Statistical Applications
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- Copyright © Applied Probability Trust 2003
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