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A simple derivation of the Tracy–Widom distribution of the maximal eigenvalue of a Gaussian unitary random matrix

A simple derivation of the Tracy–Widom distribution of the maximal eigenvalue of a Gaussian unitary random matrix

In this paper, we first briefly review some recent results on the distribution of the maximal eigenvalue of a $(N\times N)$ random matrix drawn from Gaussian ensembles. Next we focus on the Gaussian Unitary Ensemble (GUE) and by suitably adapting a method of orthogonal polynomials developed by Gross and Matytsin …