The central limit theorem for weighted minimal spanning trees on random points
Kesten, Harry ; Lee, Sungchul
Ann. Appl. Probab., Volume 6 (1996) no. 1, p. 495-527 / Harvested from Project Euclid
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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 $\sigma_{\alpha, d}^2 > 0$.
Published online : 1996-05-14
Classification:  Minimal spanning tree,  central limit theorem,  60D05,  60F05 
@article{1034968141,
     author = {Kesten, Harry and Lee, Sungchul},
     title = {The central limit theorem for weighted minimal spanning trees on
		 random points},
     journal = {Ann. Appl. Probab.},
     volume = {6},
     number = {1},
     year = {1996},
     pages = { 495-527},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1034968141}
}

Kesten, Harry; Lee, Sungchul. The central limit theorem for weighted minimal spanning trees on
		 random points. Ann. Appl. Probab., Volume 6 (1996) no. 1, pp.  495-527. http://gdmltest.u-ga.fr/item/1034968141/