# Rate of convergence of power-weighted Euclidean minimal spanning trees

Research output: Contribution to journalArticle

1 Citation (Scopus)

### Abstract

Let {Xi:i1} be i.i.d. uniform points on [-1/2,1/2]d, d2, and for 0<p<∞. Let L({X1,Xn},p) be the total weight of the minimal spanning tree on {X1,Xn} with weight function w(e)=|e|p. Then, there exist strictly positive but finite constants β(d,p), C3=C3(d,p), and C4=C4(d,p) such that for large n, C3n-1/d≤EL({X1,Xn},p)/n (d-p)/d-β(d,p)≤C4n-1/d.

Original language English 163-176 14 Stochastic Processes and their Applications 86 1 https://doi.org/10.1016/S0304-4149(99)00091-5 Published - 2000 Jan 1

### Fingerprint

Minimal Spanning Tree
Strictly positive
Weight Function
Euclidean
Rate of Convergence

### All Science Journal Classification (ASJC) codes

• Statistics and Probability
• Modelling and Simulation
• Applied Mathematics

### Cite this

@article{e98685b3beff4b9a930d8a75c34f7a09,
title = "Rate of convergence of power-weighted Euclidean minimal spanning trees",
abstract = "Let {Xi:i1} be i.i.d. uniform points on [-1/2,1/2]d, d2, and for 01,Xn},p) be the total weight of the minimal spanning tree on {X1,Xn} with weight function w(e)=|e|p. Then, there exist strictly positive but finite constants β(d,p), C3=C3(d,p), and C4=C4(d,p) such that for large n, C3n-1/d≤EL({X1,Xn},p)/n (d-p)/d-β(d,p)≤C4n-1/d.",
author = "Lee, {Sung chul}",
year = "2000",
month = "1",
day = "1",
doi = "10.1016/S0304-4149(99)00091-5",
language = "English",
volume = "86",
pages = "163--176",
journal = "Stochastic Processes and their Applications",
issn = "0304-4149",
publisher = "Elsevier",
number = "1",

}

In: Stochastic Processes and their Applications, Vol. 86, No. 1, 01.01.2000, p. 163-176.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Rate of convergence of power-weighted Euclidean minimal spanning trees

AU - Lee, Sung chul

PY - 2000/1/1

Y1 - 2000/1/1

N2 - Let {Xi:i1} be i.i.d. uniform points on [-1/2,1/2]d, d2, and for 01,Xn},p) be the total weight of the minimal spanning tree on {X1,Xn} with weight function w(e)=|e|p. Then, there exist strictly positive but finite constants β(d,p), C3=C3(d,p), and C4=C4(d,p) such that for large n, C3n-1/d≤EL({X1,Xn},p)/n (d-p)/d-β(d,p)≤C4n-1/d.

AB - Let {Xi:i1} be i.i.d. uniform points on [-1/2,1/2]d, d2, and for 01,Xn},p) be the total weight of the minimal spanning tree on {X1,Xn} with weight function w(e)=|e|p. Then, there exist strictly positive but finite constants β(d,p), C3=C3(d,p), and C4=C4(d,p) such that for large n, C3n-1/d≤EL({X1,Xn},p)/n (d-p)/d-β(d,p)≤C4n-1/d.

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U2 - 10.1016/S0304-4149(99)00091-5

DO - 10.1016/S0304-4149(99)00091-5

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SP - 163

EP - 176

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

SN - 0304-4149

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