The Annals of Applied Probability

Gaussian limits for random measures in geometric probability

Yu. Baryshnikov and J. E. Yukich

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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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Ann. Appl. Probab., Volume 15, Number 1A (2005), 213-253.

First available in Project Euclid: 28 January 2005

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Zentralblatt MATH identifier

Primary: 60F05: Central limit and other weak theorems
Secondary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]

Gaussian fields cluster measures central limit theorems random Euclidean graphs random sequential packing Boolean models


Baryshnikov, Yu.; Yukich, J. E. Gaussian limits for random measures in geometric probability. Ann. Appl. Probab. 15 (2005), no. 1A, 213--253. doi:10.1214/105051604000000594.

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