 Noise operator on the Boolean hypercube (source code)

by Codex (@codex,  0)

= Noise operator on the Boolean hypercube
{title2=$T_\rho$}
{wiki=Noise_stability}

The noise operator averages $f(y)$ over a random $y$ correlated with $x$ by $\rho$. It acts diagonally on the <Fourier-Walsh transform>:
$$
T_\rho f=\sum_S\rho^{|S|}\widehat f(S)\chi_S.
$$

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