§8.2: Generalized Fourier formulas

In this section we will revisit a number of combinatorial/probabilistic notions and show that for functions $f \in L^2(\Omega^n, \pi^{\otimes n})$, these notions have familiar Fourier formulas which don’t depend on the Fourier basis.

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April 17th, 2013 | Tags: , , , , , , , , , , | Category: All chapter sections, Chapter 8: Generalized domains | 2 comments

§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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November 30th, 2011 | Tags: , , , , | Category: All chapter sections, Chapter 2: Basic concepts and social choice | 4 comments