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

^*Corresponding author for this work

Einstein Institute of Mathematics

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

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.

Keywords

Discrete Fourier analysis
Entropy
Influence
Probabilistic combinatorics

Access to Document

10.1016/j.disc.2012.07.031

Cite this

@article{7753eda26522456fa59ba04fd8fdf73d,

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",

month = nov,

day = "28",

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

language = "אנגלית",

volume = "312",

pages = "3364--3372",

journal = "Discrete Mathematics",

issn = "0012-365X",

publisher = "Elsevier B.V.",

number = "22",

}

TY - JOUR

T1 - A note on the Entropy/Influence conjecture

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 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:84865084734

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

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this