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arXiv · 1203.1024

The Janson inequalities for general up-sets

Oliver Riordan·Lutz Warnke
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Abstract

Janson and Janson, Luczak and Rucinski proved several inequalities for the lower tail of the distribution of the number of events that hold, when all the events are up-sets (increasing events) of a special form - each event is the intersection of some subset of a single set of independent events (i.e., a principal up-set). We show that these inequalities in fact hold for arbitrary up-sets, by modifying existing proofs to use only positive correlation, avoiding the need to assume positive correlation conditioned on one of the events.

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Oliver Riordan, Lutz Warnke. 2012-03-05. The Janson inequalities for general up-sets. https://doi.org/10.1002/rsa.20506

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