## Electronic Communications in Probability

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

Nicholas Weininger

#### 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

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