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The central limit theorem for Euclidean minimal spanning trees II

Part of: Limit theorems Special processes Graph theory Geometric probability and stochastic geometry

Published online by Cambridge University Press:  01 July 2016

Sungchul Lee
Sungchul Lee*
Affiliation:
Yonsei University
*
∗ Postal address: Department of Mathematics, Yonsei University, Seoul 120-749, Korea. Email address: sungchul@ bubble.yonsei.ac.kr
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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).

Keywords

Minimal spanning treecentral limit theoremcontinuum percolation

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry 60F05: Central limit and other weak theorems
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory 05C05: Trees 90C27: Combinatorial optimization
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 31 , Issue 4 , December 1999 , pp. 969 - 984
Copyright
Copyright © Applied Probability Trust 1999 

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