Slepian's lemma

In probability theory, Slepian's lemma (1962), named after David Slepian, is a Gaussian comparison inequality. It states that for Gaussian random variables ${\displaystyle X=(X_{1},\dots ,X_{n})}$ and ${\displaystyle Y=(Y_{1},\dots ,Y_{n})}$ in ${\displaystyle \mathbb {R} ^{n}}$ satisfying ${\displaystyle E[X]=E[Y]=0}$,

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