The central limit theorem for Euclidean minimal spanning trees I I

Lee, Sungchul

Ann. Appl. Probab., Tome 7 (1997) no. 1, p. 996-1020 / Harvested from Project Euclid

Résumé

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

Détail

Publié le : 1997-11-14
Classification:  Minimal spanning tree,  central limit theorem,  continuum percolation,  60D05,  60F05,  60K35,  05C05,  90C27