Elsevier

Discrete Mathematics

Volume 312, Issue 22, 28 November 2012, Pages 3364-3372
Discrete Mathematics

A note on the Entropy/Influence conjecture

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Abstract

The Entropy/Influence conjecture, raised by Friedgut and Kalai (1996) [9], 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.

Keywords

Entropy
Influence
Discrete Fourier analysis
Probabilistic combinatorics

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