On the maximal domain of attraction of Tracy-Widom distribution for Gaussian unitary ensembles

The asymptotic distribution of the largest eigenvalue of various classes of random matrices has been shown to have the Tracy-Widom distribution. In this article, we prove that the standardised maximum of an independent and identically distributed sequence of random variables having the Tracy-Widom distribution arising from the Gaussian unitary ensemble belongs to the Gumbel domain of attraction.