The limit distribution of the largest nearest-neighbour link in the unit d-cube

Let I * Ip denote the p-norm on Rd, d > 2, 1 _ p < oo. For n points drawn independently and uniformly from the unit d-cube, we obtain the limit distribution of the largest nearest-neighbour link (with respect to I Ip) in the cases (1) d = 2, 1 _ p _ oo; (2) d = 3, p = 1, 2, oo and (3) d _ 4, p = oo.