Lower large deviations for geometric functionals

Christian Hirsch*, Benedikt Jahnel, Andras Tobias

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

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This work develops a methodology for analyzing large-deviation lower tails associated with geometric functionals computed on a homogeneous Poisson point process. The technique applies to characteristics expressed in terms of stabilizing score functions exhibiting suitable monotonicity properties. We apply our results to clique counts in the random geometric graph, intrinsic volumes of Poisson-Voronoi cells, as well as power-weighted edge lengths in the random geometric, k-nearest neighbor and relative neighborhood graph.

Original languageEnglish
Article number41
Pages (from-to)1-12
Number of pages12
JournalElectronic communications in probability
Publication statusPublished - 2020


  • large deviations
  • lower tails
  • stabilizing functionals
  • random geometric graph
  • k-nearest neighbor graph
  • relative neighborhood graph
  • Voronoi tessellation
  • clique count

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