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Covering random points in a unit disk
Published online by Cambridge University Press: 01 July 2016
Abstract
Let D be the punctured unit disk. It is easy to see that no pair x, y in D can cover D in the sense that D cannot be contained in the union of the unit disks centred at x and y. With this fact in mind, let Vn = {X1, X2, …, Xn}, where X1, X2, … are random points sampled independently from a uniform distribution on D. We prove that, with asymptotic probability 1, there exist two points in Vn that cover all of Vn.
MSC classification
- Type
- Stochastic Geometry and Statistical Applications
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- Copyright © Applied Probability Trust 2008
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