Abstract
We establish Gaussian limits for general measures induced by binomial and Poisson point processes in d-dimensional space. The limiting Gaussian field has a covariance functional which depends on the density of the point process. The general results are used to deduce central limit theorems for measures induced by random graphs (nearest neighbor, Voronoi and sphere of influence graph), random sequential packing models (ballistic deposition and spatial birth-growth models) and statistics of germ-grain models.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 213-253 |
| Number of pages | 41 |
| Journal | Annals of Applied Probability |
| Volume | 15 |
| Issue number | 1 A |
| DOIs | |
| State | Published - Feb 2005 |
| Externally published | Yes |
Keywords
- Boolean models
- Central limit theorems
- Cluster measures
- Gaussian fields
- Random Euclidean graphs
- Random sequential packing
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty