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2003 Positive correlation for increasing events with disjoint dependencies does not imply positive correlation for all increasing events
Nicholas Weininger
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Electron. Commun. Probab. 8: 99-101 (2003). DOI: 10.1214/ECP.v8-1078

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.

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Nicholas Weininger. "Positive correlation for increasing events with disjoint dependencies does not imply positive correlation for all increasing events." Electron. Commun. Probab. 8 99 - 101, 2003. https://doi.org/10.1214/ECP.v8-1078

Information

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

zbMATH: 1060.60007
MathSciNet: MR1993997
Digital Object Identifier: 10.1214/ECP.v8-1078

Subjects:
Primary: 60C05

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