## Electronic Communications in Probability

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

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

#### 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