The Annals of Applied Probability

The central limit theorem for Euclidean minimal spanning trees I I

Sungchul Lee

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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 $N({X_1, \dots, X_n}; \alpha)$.

Article information

Ann. Appl. Probab., Volume 7, Number 4 (1997), 996-1020.

First available in Project Euclid: 29 January 2003

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Zentralblatt MATH identifier

Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65] 60F05: Central limit and other weak theorems
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 05C05: Trees 90C27: Combinatorial optimization

Minimal spanning tree central limit theorem continuum percolation


Lee, Sungchul. The central limit theorem for Euclidean minimal spanning trees I I. Ann. Appl. Probab. 7 (1997), no. 4, 996--1020. doi:10.1214/aoap/1043862422.

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