Moderate deviations for some point measures in geometric probability

Yu Baryshnikov, P. Eichelsbacher, T. Schreiber, J. E. Yukich

Research output: Contribution to journalArticlepeer-review


Functionals in geometric probability are often expressed as sums of bounded functions exhibiting exponential stabilization. Methods based on cumulant techniques and exponential modifications of measures show that such functionals satisfy moderate deviation principles. This leads to moderate deviation principles and laws of the iterated logarithm for random packing models as well as for statistics associated with germ-grain models and k nearest neighbor graphs.

Original languageEnglish (US)
Pages (from-to)422-446
Number of pages25
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Issue number3
StatePublished - Jun 2008
Externally publishedYes


  • Laws of the iterated logarithm
  • Moderate deviations
  • Random Euclidean graphs
  • Random sequential packing

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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