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Tracy-Widom documentation variance #49

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lazarusA opened this issue Aug 12, 2019 · 2 comments
Closed

Tracy-Widom documentation variance #49

lazarusA opened this issue Aug 12, 2019 · 2 comments

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@lazarusA
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lazarusA commented Aug 12, 2019

It says the following:

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.

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

Even though, for the calculation of the largest eigenvalue normalized it doesn't change anything.

@dlfivefifty
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I’m happy to merge a PR fixing it

@lazarusA
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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.

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