Rate of convergence of power-weighted Euclidean minimal spanning trees

Sungchul Lee

doi:10.1016/S0304-4149(99)00091-5

Rate of convergence of power-weighted Euclidean minimal spanning trees

Sungchul Lee

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

Let {X_i:i1} be i.i.d. uniform points on [-1/2,1/2]^d, d2, and for 0<p<∞. Let L({X₁,X_n},p) be the total weight of the minimal spanning tree on {X₁,X_n} 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,X_n},p)/n ^(d-p)/d-β(d,p)≤C₄n^-1/d.

Original language	English
Pages (from-to)	163-176
Number of pages	14
Journal	Stochastic Processes and their Applications
Volume	86
Issue number	1
DOIs	https://doi.org/10.1016/S0304-4149(99)00091-5
Publication status	Published - 2000 Mar

Bibliographical note

Funding Information:
Supported by a Yonsei University Research Grant.

All Science Journal Classification (ASJC) codes

Statistics and Probability
Modelling and Simulation
Applied Mathematics

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10.1016/S0304-4149(99)00091-5

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.",

author = "Sungchul Lee",

note = "Funding Information: Supported by a Yonsei University Research Grant. ",

year = "2000",

month = mar,

doi = "10.1016/S0304-4149(99)00091-5",

language = "English",

volume = "86",

pages = "163--176",

journal = "Stochastic Processes and their Applications",

issn = "0304-4149",

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TY - JOUR

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

AU - Lee, Sungchul

N1 - Funding Information: Supported by a Yonsei University Research Grant.

PY - 2000/3

Y1 - 2000/3

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

M3 - Article

AN - SCOPUS:0042916481

SN - 0304-4149

VL - 86

SP - 163

EP - 176

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 1

ER -

Rate of convergence of power-weighted Euclidean minimal spanning trees

Abstract

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