The central limit theorem for euclidean minimal spanning trees II

Sungchul Lee

doi:10.1239/aap/1029955253

The central limit theorem for euclidean minimal spanning trees II

Sungchul Lee

Department of Mathematics

Research output: Contribution to journal › Article

12 Citations (Scopus)

Abstract

Let (X_i : i ≥ 1) be i.i.d. points in ℝ^d, d ≥ 2, and let T_n be a minimal spanning tree on (X₁, X_n). Let L((X₁, X_n)) be the length of T_n and for each strictly positive integer α let N((X₁, . . ., X_n); α) be the number of vertices of degree α in T_n. If the common distribution satisfies certain regularity conditions, then we prove central limit theorems for L((X₁, . . ., X_n)) and N((X₁, . . ., X_n); α). We also study the rate of convergence for EL((X₁, . . ., X_n)).

Original language	English
Pages (from-to)	969-984
Number of pages	16
Journal	Advances in Applied Probability
Volume	31
Issue number	4
DOIs	https://doi.org/10.1239/aap/1029955253
Publication status	Published - 1999 Jan 1

All Science Journal Classification (ASJC) codes

Statistics and Probability
Applied Mathematics

Access to Document

10.1239/aap/1029955253

Fingerprint Dive into the research topics of 'The central limit theorem for euclidean minimal spanning trees II'. Together they form a unique fingerprint.

Cite this

Lee, S. (1999). The central limit theorem for euclidean minimal spanning trees II. Advances in Applied Probability, 31(4), 969-984. https://doi.org/10.1239/aap/1029955253

@article{c719b63805834c4cb488b1194c8b46c0,

title = "The central limit theorem for euclidean minimal spanning trees II",

abstract = "Let (Xi : i ≥ 1) be i.i.d. points in ℝd, d ≥ 2, and let Tn be a minimal spanning tree on (X1, Xn). Let L((X1, Xn)) be the length of Tn and for each strictly positive integer α let N((X1, . . ., Xn); α) be the number of vertices of degree α in Tn. If the common distribution satisfies certain regularity conditions, then we prove central limit theorems for L((X1, . . ., Xn)) and N((X1, . . ., Xn); α). We also study the rate of convergence for EL((X1, . . ., Xn)).",

author = "Sungchul Lee",

year = "1999",

month = jan,

day = "1",

doi = "10.1239/aap/1029955253",

language = "English",

volume = "31",

pages = "969--984",

journal = "Advances in Applied Probability",

issn = "0001-8678",

publisher = "University of Sheffield",

number = "4",

}

TY - JOUR

T1 - The central limit theorem for euclidean minimal spanning trees II

AU - Lee, Sungchul

PY - 1999/1/1

Y1 - 1999/1/1

N2 - Let (Xi : i ≥ 1) be i.i.d. points in ℝd, d ≥ 2, and let Tn be a minimal spanning tree on (X1, Xn). Let L((X1, Xn)) be the length of Tn and for each strictly positive integer α let N((X1, . . ., Xn); α) be the number of vertices of degree α in Tn. If the common distribution satisfies certain regularity conditions, then we prove central limit theorems for L((X1, . . ., Xn)) and N((X1, . . ., Xn); α). We also study the rate of convergence for EL((X1, . . ., Xn)).

AB - Let (Xi : i ≥ 1) be i.i.d. points in ℝd, d ≥ 2, and let Tn be a minimal spanning tree on (X1, Xn). Let L((X1, Xn)) be the length of Tn and for each strictly positive integer α let N((X1, . . ., Xn); α) be the number of vertices of degree α in Tn. If the common distribution satisfies certain regularity conditions, then we prove central limit theorems for L((X1, . . ., Xn)) and N((X1, . . ., Xn); α). We also study the rate of convergence for EL((X1, . . ., Xn)).

UR - http://www.scopus.com/inward/record.url?scp=0033315088&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033315088&partnerID=8YFLogxK

U2 - 10.1239/aap/1029955253

DO - 10.1239/aap/1029955253

M3 - Article

AN - SCOPUS:0033315088

VL - 31

SP - 969

EP - 984

JO - Advances in Applied Probability

JF - Advances in Applied Probability

SN - 0001-8678

IS - 4

ER -