Open Access
January, 1987 On a Combinatorial Conjecture Concerning Disjoint Occurrences of Events
J. Van Den Berg, U. Fiebig
Ann. Probab. 15(1): 354-374 (January, 1987). DOI: 10.1214/aop/1176992274


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.


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J. Van Den Berg. U. Fiebig. "On a Combinatorial Conjecture Concerning Disjoint Occurrences of Events." Ann. Probab. 15 (1) 354 - 374, January, 1987.


Published: January, 1987
First available in Project Euclid: 19 April 2007

zbMATH: 0617.60011
MathSciNet: MR877608
Digital Object Identifier: 10.1214/aop/1176992274

Primary: 60C05
Secondary: 60K10 , 60K35

Keywords: combinatorial probability , Correlation inequality , Disjoint occurrences of events , finite Bernoulli sequences , FKG inequality , percolation

Rights: Copyright © 1987 Institute of Mathematical Statistics

Vol.15 • No. 1 • January, 1987
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