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November 1997 The central limit theorem for Euclidean minimal spanning trees I I
Sungchul Lee
Ann. Appl. Probab. 7(4): 996-1020 (November 1997). DOI: 10.1214/aoap/1043862422

Abstract

Let ${X_i: i \geq 1}$ be i.i.d. with uniform distribution $[- 1/2, 1/2]^d, d \geq 2$, and let $T_n$ be a minimal spanning tree on ${X_1, \dots, X_n}$. For each strictly positive integer $\alpha$, let $N({X_1, \dots, X_n}; \alpha)$ be the number of vertices of degree $\alpha$ in $T_n$. Then, for each $\alpha$ such that $P(N({X_1, \dots, X_{\alpha+1}}; \alpha) = 1) > 0$, we prove a central limit theorem for $N({X_1, \dots, X_n}; \alpha)$.

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Sungchul Lee. "The central limit theorem for Euclidean minimal spanning trees I I." Ann. Appl. Probab. 7 (4) 996 - 1020, November 1997. https://doi.org/10.1214/aoap/1043862422

Information

Published: November 1997
First available in Project Euclid: 29 January 2003

zbMATH: 0892.60034
MathSciNet: MR1484795
Digital Object Identifier: 10.1214/aoap/1043862422

Subjects:
Primary: 60D05 , 60F05
Secondary: 05C05 , 60K35 , 90C27

Keywords: central limit theorem , continuum percolation , Minimal spanning tree

Rights: Copyright © 1997 Institute of Mathematical Statistics

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Vol.7 • No. 4 • November 1997
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