Theorems of KKL, friedgut, and talagrand via random restrictions and log-sobolev inequality

Esty Kelman, Subhash Khot, Guy Kindler, Dor Minzer, Muli Safra

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

Abstract

We give alternate proofs for three related results in analysis of Boolean functions, namely the KKL Theorem, Friedgut’s Junta Theorem, and Talagrand’s strengthening of the KKL Theorem. We follow a new approach: looking at the first Fourier level of the function after a suitable random restriction and applying the Log-Sobolev inequality appropriately. In particular, we avoid using the hypercontractive inequality that is common to the original proofs. Our proofs might serve as an alternate, uniform exposition to these theorems and the techniques might benefit further research.

Original languageAmerican English
Title of host publication12th Innovations in Theoretical Computer Science Conference, ITCS 2021
EditorsJames R. Lee
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Pages26:1-26:17
Number of pages17
ISBN (Electronic)9783959771771
DOIs
StatePublished - 1 Feb 2021
Event12th Innovations in Theoretical Computer Science Conference, ITCS 2021 - Virtual, Online
Duration: 6 Jan 20218 Jan 2021

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume185
ISSN (Print)1868-8969

Conference

Conference12th Innovations in Theoretical Computer Science Conference, ITCS 2021
CityVirtual, Online
Period6/01/218/01/21

Bibliographical note

Publisher Copyright:
© Esty Kelman, Subhash Khot, Guy Kindler, Dor Minzer, and Muli Safra.

Keywords

  • Fourier analysis
  • Hypercontractivity
  • Log-sobolev inequality

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