The central limit theorem for Euclidean minimal spanning trees II

Let (X-i : i greater than or equal to 1) be i.i.d. points in R-d, d greater than or equal to 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 ct let N({X-1,..., X-n}; alpha) be the number of vertices of degree alpha 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}; alpha). We also study the rate of convergence for EL ({X-1,..., X-n}) AMS 1991 Subject Classification: Primary 60D05; 60F05 Secondary 60K35; 05C05; 90C27.