A Note on the Entropy/Influence Conjecture

Details A Note on the Entropy/Influence Conjecture A Note on the Entropy/Influence Conjecture

2011-05-13

arxiv.org/abs/1105.2651v1

Mathematics

Combinatorics

12 pages

Scientific paper

The entropy/influence conjecture, raised by Friedgut and Kalai in 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.

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