TY - JOUR

T1 - Local central limit theorems in stochastic geometry

AU - Penrose, Mathew D

AU - Peres, Y

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=83255192897&partnerID=8YFLogxK

UR - http://ejp.ejpecp.org/article/view/968/1155

M3 - Article

SN - 1083-6489

VL - 16

SP - 2509

EP - 2544

JO - Electronic Journal of Probability

JF - Electronic Journal of Probability

M1 - 91

ER -