Gaussian limits for random measures in geometric probability

Yu Baryshnikov, J. E. Yukich

Research output: Contribution to journalArticle

46 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)213-253
Number of pages41
JournalAnnals of Applied Probability
Volume15
Issue number1 A
DOIs
Publication statusPublished - Feb 1 2005
Externally publishedYes

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Geometric Probability
Random Measure
Random Graphs
Gaussian Fields
Poisson Point Process
Voronoi
Ballistics
Point Process
Growth Model
Central limit theorem
Packing
Deduce
Nearest Neighbor
Limiting
Statistics
Model
Point process
Random graphs

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Gaussian limits for random measures in geometric probability. / Baryshnikov, Yu; Yukich, J. E.

In: Annals of Applied Probability, Vol. 15, No. 1 A, 01.02.2005, p. 213-253.

Research output: Contribution to journalArticle

Baryshnikov, Yu ; Yukich, J. E. / Gaussian limits for random measures in geometric probability. In: Annals of Applied Probability. 2005 ; Vol. 15, No. 1 A. pp. 213-253.
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