The central limit theorem for Euclidean minimal spanning trees I

Sungchul Lee

The central limit theorem for Euclidean minimal spanning trees I

Sungchul Lee

Department of Mathematics

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

39 Citations (Scopus)

Abstract

Let {X_i: i ≥ 1} be i.i.d. with uniform distribution [- 1/2, 1/2]^d, d ≥ 2, and let T_n be a minimal spanning tree on {X₁,..., X_n}. For each strictly positive integer α, let N({X₁,..., X_n}; α) be the number of vertices of degree α in T_n. Then, for each α such that P(N({X₁,..., X_α+1}; α) = 1) > 0, we prove a central limit theorem for N({X₁,..., X_n}; α).

Original language	English
Pages (from-to)	996-1020
Number of pages	25
Journal	Annals of Applied Probability
Volume	7
Issue number	4
Publication status	Published - 1997 Nov

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

Cite this

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abstract = "Let {Xi: i ≥ 1} be i.i.d. with uniform distribution [- 1/2, 1/2]d, d ≥ 2, and let Tn be a minimal spanning tree on {X1,..., Xn}. For each strictly positive integer α, let N({X1,..., Xn}; α) be the number of vertices of degree α in Tn. Then, for each α such that P(N({X1,..., Xα+1}; α) = 1) > 0, we prove a central limit theorem for N({X1,..., Xn}; α).",

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N2 - Let {Xi: i ≥ 1} be i.i.d. with uniform distribution [- 1/2, 1/2]d, d ≥ 2, and let Tn be a minimal spanning tree on {X1,..., Xn}. For each strictly positive integer α, let N({X1,..., Xn}; α) be the number of vertices of degree α in Tn. Then, for each α such that P(N({X1,..., Xα+1}; α) = 1) > 0, we prove a central limit theorem for N({X1,..., Xn}; α).

AB - Let {Xi: i ≥ 1} be i.i.d. with uniform distribution [- 1/2, 1/2]d, d ≥ 2, and let Tn be a minimal spanning tree on {X1,..., Xn}. For each strictly positive integer α, let N({X1,..., Xn}; α) be the number of vertices of degree α in Tn. Then, for each α such that P(N({X1,..., Xα+1}; α) = 1) > 0, we prove a central limit theorem for N({X1,..., Xn}; α).

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The central limit theorem for Euclidean minimal spanning trees I

Abstract

All Science Journal Classification (ASJC) codes

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