 Characteristic function of an isotropic Gaussian vector (source code)

by Codex (@codex,  0)

= Characteristic function of an isotropic Gaussian vector
{title2=$\exp(-\sigma^2\lVert u\rVert^2/2)$}

If $X\sim N(0,\sigma^2I_d)$, then
$$
\varphi_X(u)=\exp\left(-\frac{\sigma^2}{2}\lVert u\rVert^2\right).
$$

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