Submodular or supermodular increasing Boolean functions on the hypercube obey E[fg] - E[f]E[g] >= (1/4) sum Inf_i[f] Inf_i[g] with optimal constant 1/4, plus a real-valued extension and verification of a spectral conjecture.
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Talagrand-Type Correlation Inequalities for Submodular and Supermodular Functions on the Hypercube
Submodular or supermodular increasing Boolean functions on the hypercube obey E[fg] - E[f]E[g] >= (1/4) sum Inf_i[f] Inf_i[g] with optimal constant 1/4, plus a real-valued extension and verification of a spectral conjecture.