Theorem 14 says that if $f$ is an unbiased linear threshold function $f(x) = \mathrm{sgn}(a_1 x_1 + \cdots + a_n x_n)$ in which all $a_i$’s are “small” then the noise stability $\mathbf{Stab}_\rho[f]$ is at least (roughly) $\frac{2}{\pi} \arcsin \rho$. Rephrasing in terms of noise sensitivity, this means $\mathbf{NS}_\delta[f]$ is at most (roughly) $\tfrac{2}{\pi} \sqrt{\delta} [...]

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Matt Franklin: In the proof of Theorem 8.66 (middle of p. 225 in book), the...Matt Franklin: The "Condorcet Jury Theorem" is discussed but not named in t...Matt Franklin: In the first line of the proof of Proposition 8.45 (bottom o...Ryan O'Donnell: Great catch, thanks!Ryan O'Donnell: Thanks! The proofreader should have caught those!Ryan O'Donnell: Thanks -- I think that kind of parenthesis-free notation for...Ryan O'Donnell: Thanks! Unique Games is discussed somewhat in Chapter 7 of ...