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 Dec

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Applied Mathematics

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