A Strong Law for the Longest Edge of the Minimal Spanning Tree

Penrose, Mathew D.

Ann. Probab., Tome 27 (1999) no. 1, p. 246-260 / Harvested from Project Euclid

Résumé

Suppose $X_1, X_2, X_3,\ldots$ are independent random points in $\mathbf{R}^d,d\geq 2$, with common density $f$, having connected compact support $\Omega$ with smooth boundary $\partial\Omega$, with $f|_{\Omega}$ continuous. Let $M_{n}$denote the smallest $r$ such that the union of balls of diameter $r$ centered at the first $n$ points is connected. Let $\theta$ denote the volume of the unit ball. Then as $n\to\infty$,

Détail

Publié le : 1999-01-14
Classification:  Geometric probability,  connectedness,  minimal spanning tree,  extreme values,  60D05,  60G70,  60F15