Gaussian limits for random measures in geometric probability

Details Gaussian limits for random measures in geometric probability Gaussian limits for random measures in geometric probability

2005-03-23

arxiv.org/abs/math/0503474v1

Annals of Applied Probability 2005, Vol. 15, No. 1A, 213-253

Mathematics

Probability

Published at http://dx.doi.org/10.1214/105051604000000594 in the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

10.1214/105051604000000594

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.

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