Boundary domination and the distribution of the largest nearest-neighbor link in higher dimensions. (English) Zbl 0612.60010
Authors’ abstract: For a sample of points drawn uniformly from either the d-dimensional torus or the d-cube, \(d\geq 2\), we give limiting distributions for the largest of the nearest-neighbor links. For \(d\geq 3\) the behavior in the torus is proved to be different from the behavior in the cube. The results given also settle a conjecture of N. Henze [J. Appl. Probab. 19, 344-354 (1982; Zbl 0484.62034)] and throw light on the choice of the cube or torus in some probabilistic models of computational complexity of geometrical algorithms.
Reviewer: J.C.Massé
MSC:
60D05 | Geometric probability and stochastic geometry |
62E20 | Asymptotic distribution theory in statistics |