A Note on the Entropy/Influence Conjecture
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entropy
influence
discrete fourier analysis
probabilistic combinatorics
Statistics and Probability
influence
discrete fourier analysis
probabilistic combinatorics
Statistics and Probability
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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, and prove a variant of the conjecture for functions with an extremely low Fourier weight on the “high” levels.
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2012-11-28
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Discrete Mathematics
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At the time of publication, author Elchanan Mossel was affiliated with the University of California, Berkeley. Currently, he is a faculty member at the Statistics Department at the University of Pennsylvania.