1 results
Nearest neighbors and Voronoi regions in certain point processes
-
- Journal:
- Advances in Applied Probability / Volume 15 / Issue 4 / December 1983
- Published online by Cambridge University Press:
- 01 July 2016, pp. 726-751
- Print publication:
- December 1983
-
- Article
- Export citation
-
We investigate, for several models of point processes, the (random) number N of points which have a given point as their nearest neighbor. The largedimensional limit of Poisson processes is treated by considering
for n points independently and uniformly distributed in a d-dimensional cube of volume n and showing that 
Poisson (λ= 1). An asymptotic Poisson (λ= 1) distribution also holds for many of the other models. On the other hand, we find that 
. Related results concern the (random) volume, 
, of a Voronoi polytope (or Dirichlet cell) in the cube model; we find that 
while 
for 
Poisson (λ= 1). An asymptotic Poisson (λ= 1) distribution also holds for many of the other models. On the other hand, we find that 
. Related results concern the (random) volume, 
, of a Voronoi polytope (or Dirichlet cell) in the cube model; we find that 
while 
