The central limit theorem for euclidean minimal spanning trees ii

Sungchul Lee

doi:10.1017/S0001867800009551

The central limit theorem for euclidean minimal spanning trees ii

Sungchul Lee

Department of Mathematics

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

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/10.1017/S0001867800009551
Publication status	Published - 1999 Dec

All Science Journal Classification (ASJC) codes

Statistics and Probability
Applied Mathematics

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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",

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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}).

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JO - Advances in Applied Probability

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The central limit theorem for euclidean minimal spanning trees ii

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