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.
Description
[1006.3523] Local central limit theorems in stochastic geometry
%0 Generic
%1 penrose2010local
%A Penrose, Mathew D.
%A Peres, Yuval
%D 2010
%K dependant_CLT local_CLT percolation
%T Local central limit theorems in stochastic geometry
%U http://arxiv.org/abs/1006.3523
%X 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.
@misc{penrose2010local,
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.
},
added-at = {2010-06-23T18:39:35.000+0200},
author = {Penrose, Mathew D. and Peres, Yuval},
biburl = {https://www.bibsonomy.org/bibtex/2e69f6e93bb9af2fe58fb8ebd437954fd/peter.ralph},
description = {[1006.3523] Local central limit theorems in stochastic geometry},
interhash = {12e6e2ea4ebe64f08d284f18221c20b1},
intrahash = {e69f6e93bb9af2fe58fb8ebd437954fd},
keywords = {dependant_CLT local_CLT percolation},
note = {cite arxiv:1006.3523
Comment: 31 Pages},
timestamp = {2010-06-23T18:39:35.000+0200},
title = {Local central limit theorems in stochastic geometry},
url = {http://arxiv.org/abs/1006.3523},
year = 2010
}