The central limit theorem for Euclidean minimal spanning trees I

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Abstract

Let {Xi: i ≥ 1} be i.i.d. with uniform distribution [- 1/2, 1/2]d, d ≥ 2, and let Tn be a minimal spanning tree on {X1,..., Xn}. For each strictly positive integer α, let N({X1,..., Xn}; α) be the number of vertices of degree α in Tn. Then, for each α such that P(N({X1,..., Xα+1}; α) = 1) > 0, we prove a central limit theorem for N({X1,..., Xn}; α).

Original languageEnglish
Pages (from-to)996-1020
Number of pages25
JournalAnnals of Applied Probability
Volume7
Issue number4
Publication statusPublished - 1997 Nov

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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