文章基本信息

标题：Theorems of KKL, Friedgut, and Talagrand via Random Restrictions and Log-Sobolev Inequality
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作者：Esty Kelman ; Subhash Khot ; Guy Kindler 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2021
卷号：185
页码：26:1-26:17
DOI：10.4230/LIPIcs.ITCS.2021.26
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：We give alternate proofs for three related results in analysis of Boolean functions, namely the KKL Theorem, Friedgutâs Junta Theorem, and Talagrandâs 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.
关键词：Fourier Analysis; Hypercontractivity; Log-Sobolev Inequality