The subject of Gaussian space is too enormous to be surveyed here; some recommended texts include Janson [Jan97] and Bogachev [Bog98], the latter having an extremely thorough bibliography.
[...]


The subject of Gaussian space is too enormous to be surveyed here; some recommended texts include Janson [Jan97] and Bogachev [Bog98], the latter having an extremely thorough bibliography. [...] The Majority Is Stablest Theorem (to be proved at the end of this section) was originally conjectured in 2004 [KKMO04,KKMO07]. The motivation came from studying the approximability of the MaxCut CSP. [...] If we believe that the Majority Is Stablest Theorem should be true, then we also have to believe in its “Gaussian special case”. Let’s see what this Gaussian special case is. [...] The final destination of this chapter is a proof of the following theorem due to Mossel, O’Donnell, and Oleszkiewicz [MOO05a,MOO10], first mentioned in Chapter 5.25: Majority Is Stablest Theorem Fix $\rho \in (0,1)$. Let $f : \{1,1\}^n \to [1,1]$ have $\mathop{\bf E}[f] = 0$. Then, assuming $\mathbf{MaxInf}[f] \leq \epsilon$, or more generally that $f$ [...] 

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