✦ LIBER ✦

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

✍ Scribed by David Aldous

Publisher: Elsevier Science
Year: 1989
Tongue: English
Weight: 786 KB
Volume: 76
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(89)90316-6

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✦ Synopsis

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.