= Sub-Gaussian random vector
{title2=$\mathbb E e^{\langle a,g\rangle}\leq e^{\tau^2\|a\|_2^2/2}$}
A centered random vector is sub-Gaussian with variance proxy $\tau^2$ when the displayed inequality holds for every deterministic vector $a$. Equivalently every scalar inner product is a <sub-Gaussian random variable> with proxy $\tau^2\|a\|_2^2$. Independence of coordinates is not required. For vectors $a_j$ with <Euclidean norms> at most one, the <union bound> gives $\max_j|\langle a_j,g\rangle|\leq\tau\sqrt{2\log(2m/\delta)}$ with <probability> at least $1-\delta$. This assumption alone is weaker than concentration for all Lipschitz functions.
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