The central limit theorem for Euclidean minimal spanning trees I I

Let Xᵢ: i ≥ 1 be i.i.d. with uniform distribution [- 1/2, 1/2]ᵈ, d ≥ 2, and let Tₙ be a minimal spanning tree on X₁, , Xₙ. For each strictly positive integer α, let N(X₁, , Xₙ; α) be the number of vertices of degree α in Tₙ. Then, for each α such that P(N(X₁, , Xα+1; α) = 1) > 0, we prove a central limit theorem for N(X₁, , Xₙ; α).