Rate of convergence of power-weighted Euclidean minimal spanning trees

Let {Xi: i[greater-or-equal, slanted]1} be i.i.d. uniform points on [-1/2,1/2]d, d[greater-or-equal, slanted]2, and for 0<p<[infinity]. Let L({X1,...,Xn},p) be the total weight of the minimal spanning tree on {X1,...,Xn} with weight function w(e)=ep. Then, there exist strictly positive but finite constants [beta](d,p), C3=C3(d,p), and C4=C4(d,p) such that for large n, C3n-1/d[less-than-or-equals, slant]EL({X1,...,Xn},p)/n(d-p)/d-[beta](d,p)[less-than-or-equals, slant]C4n-1/d.