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

   
@article{ECP1078,
	author = {Nicholas Weininger},
	title = {Positive correlation for increasing events with disjoint dependencies does not imply positive correlation for all increasing events},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {8},
	year = {2003},
	keywords = {},
	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.},
	pages = {no. 11, 99-101},
	issn = {1083-589X},
	doi = {10.1214/ECP.v8-1078},    
        url = {http://ecp.ejpecp.org/article/view/1078}}