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The Entropy/Influence conjecture, raised by Friedgut and Kalai (1996) , seeks to relate two different measures of concentration of the Fourier coefficients of a Boolean function. Roughly saying, it claims that if the Fourier spectrum is “smeared out”, then the Fourier coefficients are concentrated on “high” levels. In this note we generalize the conjecture to biased product measures on the discrete cube, and prove a variant of the conjecture for functions with an extremely low Fourier weight on the “high” levels.
© 2012. This manuscript version is made available under the CC-BY-NC-ND 4.0 license.
entropy, influence, discrete fourier analysis, probabilistic combinatorics
Keller, N., Mossel, E., & Schlank, T. (2012). A Note on the Entropy/Influence Conjecture. Discrete Mathematics, 312 (22), 3364-3372. http://dx.doi.org/10.1016/j.disc.2012.07.031
Date Posted: 27 November 2017
This document has been peer reviewed.