The Annals of Probability
- Ann. Probab.
- Volume 15, Number 1 (1987), 354-374.
On a Combinatorial Conjecture Concerning Disjoint Occurrences of Events
Recently van den Berg and Kesten have obtained a correlation-like inequality for Bernoulli sequences. This inequality, which goes in the opposite direction of the FKG inequality, states that the probability that two monotone (i.e., increasing or decreasing) events "occur disjointly" is smaller than the product of the individual probabilities. They conjecture that the monotonicity condition is immaterial, i.e., that the inequality holds for all events. In the present paper we try to make clear the intuitive meaning of the conjecture and prove some nontrivial special cases, one of which, a pure correlation inequality, is an extension of Harris' FKG inequality.
Ann. Probab., Volume 15, Number 1 (1987), 354-374.
First available in Project Euclid: 19 April 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60C05: Combinatorial probability
Secondary: 60K10: Applications (reliability, demand theory, etc.) 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Berg, J. Van Den; Fiebig, U. On a Combinatorial Conjecture Concerning Disjoint Occurrences of Events. Ann. Probab. 15 (1987), no. 1, 354--374. doi:10.1214/aop/1176992274. https://projecteuclid.org/euclid.aop/1176992274