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Tracy-Widom distribution
The probability distribution of the normalized largest eigenvalue of a random
matrix with iid Gaussian matrix elements of variance 1/2 and mean 0.
My bad. No need. For the standard ensembles is fine. I got confused by the Wishart case, where the variance should be taking into account in order to compare with the Tracy-Widom distribution.
It says the following:
but, I think that this description is only correct for$\beta = 2$ and not $\beta = 1$ , in which case it should be a variance of 1 and mean zero.
ref: https://pdfs.semanticscholar.org/df6a/a82dbd49f7646f1ca8436860ade4024246e7.pdf
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