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

Abstract

Let·_p denote the p-norm on . 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 | · |_p) in the cases ; (2) d = 3, p = 1, 2, ∞and (3) 4, p =∞.