The Annals of Probability

On a Combinatorial Conjecture Concerning Disjoint Occurrences of Events

J. Van Den Berg and U. Fiebig

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Abstract

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.

Article information

Source
Ann. Probab., Volume 15, Number 1 (1987), 354-374.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176992274

Digital Object Identifier
doi:10.1214/aop/1176992274

Mathematical Reviews number (MathSciNet)
MR877608

Zentralblatt MATH identifier
0617.60011

JSTOR
links.jstor.org

Subjects
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]

Keywords
Disjoint occurrences of events correlation inequality FKG inequality combinatorial probability percolation finite Bernoulli sequences

Citation

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


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