Quantitative relation between noise sensitivity and influences

@article{Keller2010QuantitativeRB,
  title={Quantitative relation between noise sensitivity and influences},
  author={Nathan Keller and Guy Kindler},
  journal={Combinatorica},
  year={2010},
  volume={33},
  pages={45-71}
}
A Boolean function f: {0,1}n → {0,1} is said to be noise sensitive if inserting a small random error in its argument makes the value of the function almost unpredictable. Benjamini, Kalai and Schramm [3] showed that if the sum of squares of inuences of f is close to zero then f must be noise sensitive. We show a quantitative version of this result which does not depend on n, and prove that it is tight for certain parameters. Our results hold also for a general product measure µp on the discrete… CONTINUE READING

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