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Gaussian functions / distributions / processes...

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Integrability of Gaussian sums

It is a standard fact from the theory of Gaussian processes (see e.g. the Ledoux-Talagrand book) that if $X_s$, $s \in S$, is a (centered) Gaussian process such that $Z = \sup_s X_s$ is finite almost surely … Hence here $\sigma^2 = \sup_\alpha \langle \Sigma \alpha, \alpha \rangle$ where $\Sigma$ is the covariance matrix of the Gaussian vector $X = (X_1, \ldots, X_n)$. …
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