The harmonic mean formula for probabilities of unions: applications to sparse random graphs

@article{Aldous1989TheHM,
  title={The harmonic mean formula for probabilities of unions: applications to sparse random graphs},
  author={David Aldous},
  journal={Discrete Mathematics},
  year={1989},
  volume={76},
  pages={167-176}
}
Under a symmetry condition, the probability of a union of events can be expressed in terms of the harmonic mean number of events which occur, conditioned on a specific event occurring. This leads to improvements of Boole’s inequality in settings where standard inclusion-exclusion techniques fail. Applications to asymptotic independence numbers and partition numbers of sparse random graphs are given. 

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Random Graphs

  • B. Bollobzis
  • 1985

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