### Abstract

Let {X_{i}, 1 ≤ i < ∞} be i.i.d. with uniform distribution on [0, 1]^{d} and let M(X_{1},..., X_{n};α) be min{Σ_{e∈T′}\e\α; T′ a spanning tree on {X_{1},..., X_{n}}}. Then we show that for α > 0, formula presented in distribution for some σ^{2} _{α,d} > 0.

Original language | English |
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Pages (from-to) | 495-527 |

Number of pages | 33 |

Journal | Annals of Applied Probability |

Volume | 6 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1996 Jan 1 |

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### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

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*Annals of Applied Probability*, vol. 6, no. 2, pp. 495-527. https://doi.org/10.1214/aoap/1034968141

**The central limit theorem for weighted minimal spanning trees on random points.** / Kesten, Harry; Lee, Sung chul.

Research output: Contribution to journal › Article

TY - JOUR

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

AU - Kesten, Harry

AU - Lee, Sung chul

PY - 1996/1/1

Y1 - 1996/1/1

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.

UR - http://www.scopus.com/inward/record.url?scp=0030501338&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030501338&partnerID=8YFLogxK

U2 - 10.1214/aoap/1034968141

DO - 10.1214/aoap/1034968141

M3 - Article

AN - SCOPUS:0030501338

VL - 6

SP - 495

EP - 527

JO - Annals of Applied Probability

JF - Annals of Applied Probability

SN - 1050-5164

IS - 2

ER -