The central limit theorem for euclidean minimal spanning trees II

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12 Citations (Scopus)

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 language English 969-984 16 Advances in Applied Probability 31 4 https://doi.org/10.1239/aap/1029955253 Published - 1999 Jan 1

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Minimal Spanning Tree
Strictly positive
Regularity Conditions
Central limit theorem
Euclidean
Rate of Convergence
Integer

All Science Journal Classification (ASJC) codes

• Statistics and Probability
• Applied Mathematics

Cite this

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In: Advances in Applied Probability, Vol. 31, No. 4, 01.01.1999, p. 969-984.

Research output: Contribution to journalArticle

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T1 - The central limit theorem for euclidean minimal spanning trees II

AU - Lee, Sung chul

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N2 - 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)).

AB - 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)).

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