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

Harry Kesten; Sungchul Lee

doi:10.1214/aoap/1034968141

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

Harry Kesten, Sungchul Lee

Department of Mathematics

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

64 Citations (Scopus)

Abstract

Let {X_i, 1 ≤ i < ∞} be i.i.d. with uniform distribution on [0, 1]^d and let M(X₁,..., X_n;α) be min{Σ_e∈T′\e\α; T′ a spanning tree on {X₁,..., X_n}}. Then we show that for α > 0, formula presented in distribution for some σ²_α,d > 0.

Original language	English
Pages (from-to)	495-527
Number of pages	33
Journal	Annals of Applied Probability
Volume	6
Issue number	2
DOIs	https://doi.org/10.1214/aoap/1034968141
Publication status	Published - 1996 May

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

Access to Document

10.1214/aoap/1034968141

Cite this

@article{bd91ab8d5cd74571ba6d94e6b4139117,

title = "The central limit theorem for weighted minimal spanning trees on random points",

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 σ2α,d > 0.",

author = "Harry Kesten and Sungchul Lee",

year = "1996",

month = may,

doi = "10.1214/aoap/1034968141",

language = "English",

volume = "6",

pages = "495--527",

journal = "Annals of Applied Probability",

issn = "1050-5164",

publisher = "Institute of Mathematical Statistics",

number = "2",

}

TY - JOUR

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

AU - Kesten, Harry

AU - Lee, Sungchul

PY - 1996/5

Y1 - 1996/5

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 σ2α,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 σ2α,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

SN - 1050-5164

VL - 6

SP - 495

EP - 527

JO - Annals of Applied Probability

JF - Annals of Applied Probability

IS - 2

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this