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

The Hebrew University of Jerusalem, Weizmann Institute of Science

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

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

Keywords

Discrete Fourier analysis
Entropy
Influence
Probabilistic combinatorics

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/j.disc.2012.07.031

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title = "A note on the Entropy/Influence conjecture",

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 = "Discrete Fourier analysis, Entropy, Influence, Probabilistic combinatorics",

author = "Nathan Keller and Elchanan Mossel and Tomer Schlank",

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.",

year = "2012",

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doi = "10.1016/j.disc.2012.07.031",

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AU - Keller, Nathan

AU - Mossel, Elchanan

AU - Schlank, Tomer

N1 - 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.

PY - 2012/11/28

Y1 - 2012/11/28

N2 - 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.

AB - 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.

KW - Discrete Fourier analysis

KW - Entropy

KW - Influence

KW - Probabilistic combinatorics

UR - http://www.scopus.com/inward/record.url?scp=84865084734&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2012.07.031

DO - 10.1016/j.disc.2012.07.031

M3 - مقالة

SN - 0012-365X

VL - 312

SP - 3364

EP - 3372

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 22

ER -

A note on the Entropy/Influence conjecture

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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