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The following post builds on this post; I'll begin by quoting the setting. Background from Previous Question: $\newcommand\SS{P}\newcommand\TT{Q}$Call a Gaussian probability measure $\SS$ on $\mathbb{...

$\newcommand\SS{P}\newcommand\TT{Q}$I will call a Gaussian probability measure $\SS$ on $\mathbb{R}^d$ isotropic if its covariance matrix is diagonal with non-vanishing determinant; i.e. $\Sigma_{i,i}&...