Rate of convergence of power-weighted Euclidean minimal spanning trees

Research output: Contribution to journalArticle

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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 languageEnglish
Pages (from-to)163-176
Number of pages14
JournalStochastic Processes and their Applications
Volume86
Issue number1
DOIs
Publication statusPublished - 2000 Jan 1

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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

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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.",
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Rate of convergence of power-weighted Euclidean minimal spanning trees. / Lee, Sung chul.

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

Research output: Contribution to journalArticle

TY - JOUR

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AU - Lee, Sung chul

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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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