## The Annals of Applied Probability

### The central limit theorem for weighted minimal spanning trees on random points

#### 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 $\sigma_{\alpha, d}^2 > 0$.

#### Article information

Source
Ann. Appl. Probab. Volume 6, Number 2 (1996), 495-527.

Dates
First available in Project Euclid: 18 October 2002

http://projecteuclid.org/euclid.aoap/1034968141

Digital Object Identifier
doi:10.1214/aoap/1034968141

Mathematical Reviews number (MathSciNet)
MR1398055

Zentralblatt MATH identifier
0862.60008

#### Citation

Kesten, Harry; Lee, Sungchul. The central limit theorem for weighted minimal spanning trees on random points. Ann. Appl. Probab. 6 (1996), no. 2, 495--527. doi:10.1214/aoap/1034968141. http://projecteuclid.org/euclid.aoap/1034968141.

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