# what should be the frequency distribution of the eigenvalues of a randomly generated hermitian matrix?

I'm getting the eigenvalues of a randomly generated hermitian matrix distributed like a normal probabilistic distribution(crowded in the middle values ) but my sir told me that it should be a semicircle , not a bell shaped one.

(not enough rep to upload the plot image, sorry)

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You can upload the image to imgur.com, post a link to the image, and somebody else can attach it for you... –  Guess who it is. May 5 '12 at 14:46

I think you were told wrong. The values should indeed approach the semicircle law, but only when the size goes to infinity (and I think that you need some control on the variance of the entries, but I don't really recall that now).

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so it means if i increase the size of the matrix (now is 100*100) it can approach to semicircle law? –  Aftnix May 5 '12 at 14:11
In the limit, which doesn't necessarily mean you can get it in practice. Try searching for "Wigner law". –  Martin Argerami May 5 '12 at 14:16
this graph is for a 5000x5000 matrix mathworld.wolfram.com/WignersSemicircleLaw.html –  leonbloy May 5 '12 at 14:23