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February 2005 Gaussian limits for random measures in geometric probability
Yu. Baryshnikov, J. E. Yukich
Ann. Appl. Probab. 15(1A): 213-253 (February 2005). DOI: 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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Yu. Baryshnikov. J. E. Yukich. "Gaussian limits for random measures in geometric probability." Ann. Appl. Probab. 15 (1A) 213 - 253, February 2005.


Published: February 2005
First available in Project Euclid: 28 January 2005

zbMATH: 1068.60028
MathSciNet: MR2115042
Digital Object Identifier: 10.1214/105051604000000594

Primary: 60F05
Secondary: 60D05

Keywords: Boolean models , central limit theorems , cluster measures , Gaussian fields , random Euclidean graphs , Random sequential packing

Rights: Copyright © 2005 Institute of Mathematical Statistics

Vol.15 • No. 1A • February 2005
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