@article{EJP968,
author = {Mathew Penrose and Yuval Peres},
title = {Local Central Limit Theorems in Stochastic Geometry},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {16},
year = {2011},
keywords = {Local central limit theorem; stochastic geometry; percolation; random geometric graph; nearest neighbours},
abstract = {We give a general local central limit theorem for the sum of two independent random variables, one of which satisfies a central limit theorem while the other satisfies a local central limit theorem with the same order variance. We apply this result to various quantities arising in stochastic geometry, including: size of the largest component for percolation on a box; number of components, number of edges, or number of isolated points, for random geometric graphs; covered volume for germ-grain coverage models; number of accepted points for finite-input random sequential adsorption; sum of nearest-neighbour distances for a random sample from a continuous multidimensional distribution.},
pages = {no. 91, 2509-2544},
issn = {1083-6489},
doi = {10.1214/EJP.v16-968},
url = {http://ejp.ejpecp.org/article/view/968}}