Gaussian limits for random measures in geometric probability

Yu Baryshnikov, J. E. Yukich

Research output: Contribution to journalArticlepeer-review

65 Citations (Scopus)


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
Issue number1 A
Publication statusPublished - Feb 1 2005
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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