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May 1996 The central limit theorem for weighted minimal spanning trees on random points
Harry Kesten, Sungchul Lee
Ann. Appl. Probab. 6(2): 495-527 (May 1996). DOI: 10.1214/aoap/1034968141

Abstract

Let ${X_i, 1 \leq i < \infty}$ be i.i.d. with uniform distribution on $[0, 1]^d$ and let $M(X_1, \dots, X_n; \alpha)$ be $\min {\sum_{e \epsilon T'} |e|^{\alpha}; T' \text{a spanning tree on ${X_1, \dots, X_n}$}}$. Then we show that for $\alpha > 0$, $$\frac{M(X_1, \dots, X_n; \alpha) - EM (X_1, \dots, X_n; \alpha)}{n^{(d-2 \alpha)/2d}} \to N(0, \sigma_{\alpha, d}^2)$$ in distribution for some $\sigma_{\alpha, d}^2 > 0$.

Citation

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Harry Kesten. Sungchul Lee. "The central limit theorem for weighted minimal spanning trees on random points." Ann. Appl. Probab. 6 (2) 495 - 527, May 1996. https://doi.org/10.1214/aoap/1034968141

Information

Published: May 1996
First available in Project Euclid: 18 October 2002

zbMATH: 0862.60008
MathSciNet: MR1398055
Digital Object Identifier: 10.1214/aoap/1034968141

Subjects:
Primary: 60D05 , 60F05

Keywords: central limit theorem , Minimal spanning tree

Rights: Copyright © 1996 Institute of Mathematical Statistics

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Vol.6 • No. 2 • May 1996
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