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Let $X_1, \dots, X_n$ be iid standard Gaussians. Let $X_{(1)}\leq \dots \leq X_{(n)}$ be the corresponding order statistics. I am wondering whether these order statistics are Sub-Gaussian.

Since Guassian random variables are log-concave, we have by this question that the order statistics are also log concave. However, I would like the stronger concentration that comes with being Sub-Gaussian.

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  • $\begingroup$ Doesn't this follow more or less immediately from the formula for the density of iid Gaussian order statistics in the link you provide? $\endgroup$
    – John Dawkins
    Commented Sep 5 at 16:00

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