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

Kesten, Harry ; Lee, Sungchul

Ann. Appl. Probab., Tome 6 (1996) no. 1, p. 495-527 / Harvested from Project Euclid

Résumé

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

Détail

Publié le : 1996-05-14
Classification:  Minimal spanning tree,  central limit theorem,  60D05,  60F05