A BKR Operation for Events Occurring for Disjoint Reasons with High Probability
- 23 Downloads
KeywordsBKR inequality Percolation Box set operation
Mathematics Subject Classification (2010)60C05 05A20
Unable to display preview. Download preview PDF.
We are deeply indebted to an anonymous referee for a very careful reading of two versions of this paper. The penetrating comments provided enlightened us on various measurability issues and other important, subtle points. We thank Mathew Penrose for a useful discussion and for providing some relevant references.
The work of the first author was partially supported by NSA grant H98230-15-1-0250. The second author would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the program Data Linkage and Anonymisation where part of the work on this paper was undertaken, supported by EPSRC grant no EP/K032208/1.
- Arratia R, Garibaldi S, Hales AW (2015) The van den Berg—Kesten—Reimer operator and inequality for infinite spaces. Bernoulli, to appear. arXiv:1508.05337 [math.PR]
- Goldstein L, Rinott Y (2015) Functional van den Berg–Kesten–Reimer inequalities and their Duals, with Applications. arXiv:1508.07267 [math.PR]