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Rooted edges of a minimal directed spanning tree on random points
Published online by Cambridge University Press: 01 July 2016
Abstract
For n independent, identically distributed uniform points in [0, 1]d, d ≥ 2, let Ln be the total distance from the origin to all the minimal points under the coordinatewise partial order (this is also the total length of the rooted edges of a minimal directed spanning tree on the given random points). For d ≥ 3, we establish the asymptotics of the mean and the variance of Ln, and show that Ln satisfies a central limit theorem, unlike in the case d = 2.
MSC classification
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- Stochastic Geometry and Statistical Applications
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- Copyright © Applied Probability Trust 2006
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