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 language | English |
|---|---|
| Title of host publication | 12th Innovations in Theoretical Computer Science Conference, ITCS 2021 |
| Editors | James R. Lee |
| Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |
| Pages | 26:1-26:17 |
| Number of pages | 17 |
| ISBN (Electronic) | 9783959771771 |
| DOIs | |
| State | Published - 1 Feb 2021 |
| Event | 12th Innovations in Theoretical Computer Science Conference, ITCS 2021 - Virtual, Online Duration: 6 Jan 2021 → 8 Jan 2021 |
Publication series
| Name | Leibniz International Proceedings in Informatics, LIPIcs |
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| Volume | 185 |
| ISSN (Print) | 1868-8969 |
Conference
| Conference | 12th Innovations in Theoretical Computer Science Conference, ITCS 2021 |
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| City | Virtual, Online |
| Period | 6/01/21 → 8/01/21 |
Bibliographical note
Publisher Copyright:© Esty Kelman, Subhash Khot, Guy Kindler, Dor Minzer, and Muli Safra.
Keywords
- Fourier analysis
- Hypercontractivity
- Log-sobolev inequality