The Janson inequalities for general up-sets

Details The Janson inequalities for general up-sets The Janson inequalities for general up-sets

2012-03-05

arxiv.org/abs/1203.1024v1

Mathematics

Probability

5 pages

Scientific paper

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 product of some subset of a single set of independent Bernoulli random variables (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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