Noise Stability and Correlation with Half Spaces

Benjamini, Kalai and Schramm showed that a monotone function f : {-1; 1}(n) -> {-1, 1} is noise stable if and only if it is correlated with a half-space (a set of the form {x : < x, a > <= b}). We study noise stability in terms of correlation with half-spaces for general (not necessarily monotone) functions. We show that a function f : {-...More