Statistics Papers

Document Type

Journal Article

Date of this Version

11-28-2012

Publication Source

Discrete Mathematics

Volume

312

Issue

22

Start Page

3364

Last Page

3372

DOI

10.1016/j.disc.2012.07.031

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.

Copyright/Permission Statement

© 2012. This manuscript version is made available under the CC-BY-NC-ND 4.0 license.

Comments

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.

Keywords

entropy, influence, discrete fourier analysis, probabilistic combinatorics

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Date Posted: 27 November 2017

This document has been peer reviewed.