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The Janson inequalities for general up-sets
- Source :
- Random Structures and Algorithms 46 (2015), 391-395
- Publication Year :
- 2012
-
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.<br />Comment: 5 pages. Added weighted variant
Details
- Database :
- arXiv
- Journal :
- Random Structures and Algorithms 46 (2015), 391-395
- Publication Type :
- Report
- Accession number :
- edsarx.1203.1024
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1002/rsa.20506