@article{EJP429,
author = {Mathew Penrose},
title = {Gaussian Limts for Random Geometric Measures},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {12},
year = {2007},
keywords = {Random measures},
abstract = {Given $n$ independent random marked $d$-vectors $X_i$ with a common density, define the measure $\nu_n = \sum_i \xi_i $, where $\xi_i$ is a measure (not necessarily a point measure) determined by the (suitably rescaled) set of points near $X_i$. Technically, this means here that $\xi_i$ stabilizes with a suitable power-law decay of the tail of the radius of stabilization. For bounded test functions $f$ on $R^d$, we give a central limit theorem for $\nu_n(f)$, and deduce weak convergence of $\nu_n(\cdot)$, suitably scaled and centred, to a Gaussian field acting on bounded test functions. The general result is illustrated with applications to measures associated with germ-grain models, random and cooperative sequential adsorption, Voronoi tessellation and $k$-nearest neighbours graph.},
pages = {no. 35, 989-1035},
issn = {1083-6489},
doi = {10.1214/EJP.v12-429},
url = {http://ejp.ejpecp.org/article/view/429}}