§10.5: Highlight: General sharp threshold theorems

In Chapter 8.4 we described the problem of “threshold phenomena” for monotone functions $f : \{-1,1\}^n \to \{-1,1\}$.

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§10.3: Applications of general hypercontractivity

In this section we will collect some applications of the General Hypercontractivity Theorem, including generalizations of the facts from Section 9.5.

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§8.4: $p$-biased analysis

Perhaps the most common generalized domain in analysis of boolean functions is the case of the hypercube with “biased” bits.

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