## §6.1: Notions of pseudorandomness

The most obvious spectral property of a truly random function $\boldsymbol{f} : \{-1,1\}^n \to \{-1,1\}$ is that all of its Fourier coefficients are very small (as we saw in Exercise 5.8).

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## §2.4: Noise stability

Suppose $f : \{-1,1\}^n \to \{-1,1\}$ is a voting rule for a $2$-candidate election. Making the impartial culture assumption, the $n$ voters independently and uniformly randomly choose their votes ${\boldsymbol{x}} = ({\boldsymbol{x}}_1, \dots, {\boldsymbol{x}}_n)$. Now imagine that when each voter goes to the ballot box there is some chance that their vote is misrecorded.

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