Orban and Wolfe (1982) and Kim (1999) provided the limiting distribution for linear placement statistics under null hypotheses only when one of the sample sizes goes to infinity. In this paper we prove the asymptotic normality and the weak convergence of the linear placement statistics of Orban...

Let {Xi: i[greater-or-equal, slanted]1} be i.i.d. points in , d[greater-or-equal, slanted]2, and let LMM({X1,...,Xn},p), LMST({X1,...,Xn},p), LTSP({X1,...,Xn},p), be the length of the minimal matching, the minimal spanning tree, the traveling salesman problem, respectively, on {X1,...,Xn} with...

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 0p[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...

We consider the power laws of certain limiting values in greedy lattice animals which were introduced by Cox, Gandolfi, Griffin, and Kesten (1993) and Gandolfi and Kesten (1994). We study the behavior of the limiting values as we change the parameter p.