Noise Stability and Correlation with Half Spaces

ELECTRONIC JOURNAL OF PROBABILITY, 2018.

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Abstract:

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

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