Positive correlation for increasing events with disjoint dependencies does not imply positive correlation for all increasing events
Nicholas Weininger, Rutgers University
Abstract
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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