Israel Journal of Mathematics

, Volume 131, Issue 1, pp 269–276

On the distribution of the fourier spectrum of Boolean functions


DOI: 10.1007/BF02785861

Cite this article as:
Bourgain, J. Isr. J. Math. (2002) 131: 269. doi:10.1007/BF02785861


In this paper we obtain a general lower bound for the tail distribution of the Fourier spectrum of Boolean functionsf on {1, −1}N. Roughly speaking, fixingk∈ℤ+ and assuming thatf is not essentially determined by a bounded number (depending onk) of variables, we have that\(\sum {\left| s \right| > k\left| {\hat f(S)} \right|^2 } \gtrsim k^{ - 1/2 - \varepsilon } \). The example of the majority function shows that this result is basically optimal.

Copyright information

© The Hebrew University Magnes Press 2002

Authors and Affiliations

  1. 1.School of MathematicsInstitute for Advanced StudyPrincetonUSA

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