Noise stability of functions with low influences: Invariance and optimality

  title={Noise stability of functions with low influences: Invariance and optimality},
  author={Elchanan Mossel and Ryan O'Donnell and Krzysztof Oleszkiewicz},
  journal={46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05)},
In this paper, we study functions with low influences on product probability spaces. The analysis of Boolean functions f {-1, 1}/sup n/ /spl rarr/ {-1, 1} with low influences has become a central problem in discrete Fourier analysis. It is motivated by fundamental questions arising from the construction of probabilistically checkable proofs in theoretical computer science and from problems in the theory of social choice in economics. We prove an invariance principle for multilinear polynomials… 

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