# The central limit theorem for weighted minimal spanning trees on random points

Harry Kesten, Sung chul Lee

Research output: Contribution to journalArticle

50 Citations (Scopus)

### Abstract

Let {Xi, 1 ≤ i < ∞} be i.i.d. with uniform distribution on [0, 1]d and let M(X1,..., Xn;α) be min{Σe∈T′\e\α; T′ a spanning tree on {X1,..., Xn}}. Then we show that for α > 0, formula presented in distribution for some σ2 α,d > 0.

Original language English 495-527 33 Annals of Applied Probability 6 2 https://doi.org/10.1214/aoap/1034968141 Published - 1996 Jan 1

### Fingerprint

Minimal Spanning Tree
Central limit theorem
Spanning tree

### All Science Journal Classification (ASJC) codes

• Statistics and Probability
• Statistics, Probability and Uncertainty

### Cite this

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abstract = "Let {Xi, 1 ≤ i < ∞} be i.i.d. with uniform distribution on [0, 1]d and let M(X1,..., Xn;α) be min{Σe∈T′\e\α; T′ a spanning tree on {X1,..., Xn}}. Then we show that for α > 0, formula presented in distribution for some σ2 α,d > 0.",
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In: Annals of Applied Probability, Vol. 6, No. 2, 01.01.1996, p. 495-527.

Research output: Contribution to journalArticle

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T1 - The central limit theorem for weighted minimal spanning trees on random points

AU - Kesten, Harry

AU - Lee, Sung chul

PY - 1996/1/1

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N2 - Let {Xi, 1 ≤ i < ∞} be i.i.d. with uniform distribution on [0, 1]d and let M(X1,..., Xn;α) be min{Σe∈T′\e\α; T′ a spanning tree on {X1,..., Xn}}. Then we show that for α > 0, formula presented in distribution for some σ2 α,d > 0.

AB - Let {Xi, 1 ≤ i < ∞} be i.i.d. with uniform distribution on [0, 1]d and let M(X1,..., Xn;α) be min{Σe∈T′\e\α; T′ a spanning tree on {X1,..., Xn}}. Then we show that for α > 0, formula presented in distribution for some σ2 α,d > 0.

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