The Annals of Applied Probability

Gaussian limits for random measures in geometric probability

Yu. Baryshnikov and J. E. Yukich

Full-text: Open access

Abstract

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.

Article information

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

Dates
First available in Project Euclid: 28 January 2005

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1106922327

Digital Object Identifier
doi:10.1214/105051604000000594

Mathematical Reviews number (MathSciNet)
MR2115042

Zentralblatt MATH identifier
1068.60028

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

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

Citation

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. https://projecteuclid.org/euclid.aoap/1106922327


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