A note on the Entropy/Influence conjecture

Nathan Keller; Elchanan Mossel; Tomer Schlank

doi:10.1016/j.disc.2012.07.031

A note on the Entropy/Influence conjecture

Nathan Keller, Elchanan Mossel, Tomer Schlank

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

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.

Original language	English
Pages (from-to)	3364-3372
Number of pages	9
Journal	Discrete Mathematics
Volume	312
Issue number	22
DOIs	https://doi.org/10.1016/j.disc.2012.07.031
State	Published - 28 Nov 2012
Externally published	Yes

Bibliographical note

Funding Information:
The first author was partially supported by the Koshland Center for Basic Research . The second author was supported by a DMS 0548249 (CAREER) award, by a DOD ONR grant N000141110140 , by an ISF grant 1300/08 and by a Minerva Grant. The third author was partially supported by the Hoffman program for leadership.

Funding

The first author was partially supported by the Koshland Center for Basic Research . The second author was supported by a DMS 0548249 (CAREER) award, by a DOD ONR grant N000141110140 , by an ISF grant 1300/08 and by a Minerva Grant. The third author was partially supported by the Hoffman program for leadership.

Funders	Funder number
DOD ONR	N000141110140
Koshland Center for Basic Research
Division of Mathematical Sciences	0548249
Iowa Science Foundation	1300/08

Keywords

Discrete Fourier analysis
Entropy
Influence
Probabilistic combinatorics

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10.1016/j.disc.2012.07.031

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KW - Influence

KW - Probabilistic combinatorics

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A note on the Entropy/Influence conjecture

Abstract

Bibliographical note

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Keywords

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