The subgaussian norm of a random variable $X$ is defined as $$ \| X \|_{\Psi_2} := \inf\left\{ t > 0: \mathbb{E}\exp\left( \frac{X^2}{t^2} \right) \leq 2 \right\}. $$ What does the magnitude of this norm really say? In particular, if $X$ has a large subgaussian norm, what does it really mean intuitively? Does it say anything about the behavior of the tails and the moment of $X$?
2026-04-07 05:02:04.1775538124
Intuition behind Sub-Gaussian Norms
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