Abstract
Two upward directed sets of sequences of zeroes and ones are positively correlated. We provide a lower bound on the correlation, in function of how much the two sets simultaneously depend on the same coordinates.
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References
J. Kahn, G. Kalai, andN. Linial:The influence of variables on Boolean functions, Proc. 29th IEEE FOCS, 1988, 58–80.
M. Ledoux andM. Talagrand:Probability in Banach space, Springer Verlag, 1991.
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Work partially supported by an NSF grant.