Gaussian limits for random measures in geometric probability

Yu Baryshnikov, J. E. Yukich

Research output: Contribution to journalArticlepeer-review


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 (US)
Pages (from-to)213-253
Number of pages41
JournalAnnals of Applied Probability
Issue number1 A
StatePublished - Feb 2005
Externally publishedYes


  • Boolean models
  • Central limit theorems
  • Cluster measures
  • Gaussian fields
  • Random Euclidean graphs
  • Random sequential packing

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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