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Analysis of Boolean Functions by Ryan O'Donnell

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Chapter 9 Basics of Hypercontractivity

In 1970, Bonami proved the following central result:

The Hypercontractivity Theorem. Let and let . Then for .

As stated, this theorem may look somewhat opaque. In this chapter we consider some special cases of it that are easier to understand, easier to prove, and that encompass almost all of the theorem’s ...

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