RATE OF CONVERGENCE FOR THE EUCLIDEAN MINIMUM SPANNING TREE LIMIT LAW

Let N(n) be the number of points of a Poisson point process of intensity n times the Lebesgue measure over [0,1]2 , and let L(MST)(N(n)) be the length of the optimal spanning tree connecting these N(n) points. It is well-known that there is a constant 0 < beta(MST) < infinity such that lim(n --> infinity) EL(MST)(N(n))/square-root n = beta(MST). In this paper we give the exact rate of convergence for this limiting behavior.