Electronic Communications in Probability

Positive correlation for increasing events with disjoint dependencies does not imply positive correlation for all increasing events

Nicholas Weininger

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Abstract

A probability measure $\mu$ on the lattice $2^{[n]}$ is said to be positively associated if any two increasing functions on the lattice are positively correlated with respect to $\mu$. Pemantle asked whether, in order to establish positive association for a given $\mu$, it might be sufficient to show positive correlation only for pairs of functions which depend on disjoint subsets of the ground set $[n]$. We answer Pemantle's question in the negative, by exhibiting a measure which gives positive correlation for pairs satisfying Pemantle's condition but not for general pairs of increasing functions.

Article information

Source
Electron. Commun. Probab., Volume 8 (2003), paper no. 11, 99-101.

Dates
Accepted: 18 July 2003
First available in Project Euclid: 18 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1463608895

Digital Object Identifier
doi:10.1214/ECP.v8-1078

Mathematical Reviews number (MathSciNet)
MR1993997

Zentralblatt MATH identifier
1060.60007

Subjects
Primary: 60C05: Combinatorial probability

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Weininger, Nicholas. Positive correlation for increasing events with disjoint dependencies does not imply positive correlation for all increasing events. Electron. Commun. Probab. 8 (2003), paper no. 11, 99--101. doi:10.1214/ECP.v8-1078. https://projecteuclid.org/euclid.ecp/1463608895


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