A Strong Law for the Largest Nearest-Neighbor Link on Normally Distributed Points

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dc.creatorGupta, Bhupender
dc.creatorIyer, Srikanth K.
dc.date2006-04-27
dc.date.accessioned2026-07-07T07:11:19Z
dc.date.available2026-07-07T07:11:19Z
dc.descriptionLet $n$ points be placed independently in $d-$dimensional space according to the standard $d-$dimensional normal distribution. Let $d_n$ be the longest edge length for the nearest neighbor graph on these points. We show that \[\lim_{n \rar \infty} \frac{\sqrt{\log n} d_n}{\log \log n} = \frac{d}{\sqrt{2}}, \qquad d \geq 2, {a.s.} \]
dc.description10 pages
dc.identifierhttps://arxiv.org/abs/math/0604585
dc.identifierhttp://arxiv.org/abs/math/0604585
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/111711
dc.subjectProbability
dc.titleA Strong Law for the Largest Nearest-Neighbor Link on Normally Distributed Points
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