maximum of i.i.d gaussian variable

Asked Dec 19 '20 at 19:00

Active Dec 20 '20 at 00:59

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Let $X_1,\ldots,X_n$ be a sequence of i.i.d Gaussian with mean $0$ and variance $\frac1n$, i.e. $X_i \sim\mathcal{N}(0,\frac{1}{n})$. What is the limit behavior of $Z=\max_i X_i$.

like $\lim_{n\rightarrow \infty} \frac{Z}{n^\alpha (\log n)^\beta}=C$ for some $\alpha $, $\beta$ and $C>0$

edited Dec 19 '20 at 20:05

Stefan

asked Dec 19 '20 at 19:00

shab z

It is not clear why you have the variance of $\frac1n$, as it will lead to $Z \to 0$. But an earlier question and answer deals with the maximum of standard Gaussians and you can easily translate it to your version – Henry Dec 22 '20 at 02:52

maximum of i.i.d gaussian variable

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