The central limit theorem for Euclidean minimal spanning trees II

Abstract

Let X i : i ≥ 1 be i.i.d. points in ℝ d , d ≥ 2, and let T n be a minimal spanning tree on X 1 ,…, X n . Let L ( X 1 ,…, X n ) be the length of T n and for each strictly positive integer α let N ( X 1 ,…, X n ;α) be the number of vertices of degree α in T n . If the common distribution satisfies certain regularity conditions, then we prove central limit theorems for L ( X 1 ,…, X n ) and N ( X 1 ,…, X n ;α). We also study the rate of convergence for E L ( X 1 ,…, X n ).

Locations

• Advances in Applied Probability - View
• Project Euclid (Cornell University) - View - PDF