The central limit theorem for euclidean minimal spanning trees II

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Abstract

Let (Xi : i ≥ 1) be i.i.d. points in ℝd, d ≥ 2, and let Tn be a minimal spanning tree on (X1, Xn). Let L((X1, Xn)) be the length of Tn and for each strictly positive integer α let N((X1, . . ., Xn); α) be the number of vertices of degree α in Tn. If the common distribution satisfies certain regularity conditions, then we prove central limit theorems for L((X1, . . ., Xn)) and N((X1, . . ., Xn); α). We also study the rate of convergence for EL((X1, . . ., Xn)).

Original languageEnglish
Pages (from-to)969-984
Number of pages16
JournalAdvances in Applied Probability
Volume31
Issue number4
DOIs
Publication statusPublished - 1999 Jan 1

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Applied Mathematics

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