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} [...]

## Recent comments

Ryan O'Donnell: That's two more -- thank you very much!Ryan O'Donnell: Thanks!Ryan O'Donnell: Yes, I'll change "third" to "subsequent".Ryan O'Donnell: Thanks!Matt Franklin: There may be two small typos in the proof of Corollary 9.32 ...Matt Franklin: Small typo at the end of the proof of Theorem 9.28 (p. 264 i...Matt Franklin: Small typo at the end of the proof of Proposition 9.19 (p. 2...