A note on the Entropy/Influence conjecture

Nathan Keller, Elchanan Mossel*, Tomer Schlank

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-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 languageAmerican English
Pages (from-to)3364-3372
Number of pages9
JournalDiscrete Mathematics
Volume312
Issue number22
DOIs
StatePublished - 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

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