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: Maybe two small typos in the proof of Corollary 11.67 (p. 36...Ryan O'Donnell: I see your point, although in some sense this distinction be...Ryan O'Donnell: Thank you!Ryan O'Donnell: Yep, thanks!Ryan O'Donnell: Great catch, thanks!Matt Franklin: Maybe two small typos in last sentence before Borell's Isope...Matt Franklin: maybe small typo in Remark 11.11 (p. 328 in book): $z \tild...