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In your Mathematica lab, you have explored the statistics of the
eigenvalues of a large nxn random matrix.
n=1000; A = Table[Random[]-1/2,{n},{n}];
vec[z_]:={Re[z],Im[z]}; EV=Eigenvalues[A];
Show[Graphics[Table[Point[vec[EV[[i]]]],{i,Length[EV]}]],
AspectRatio->1]
You saw that the eigevanvalues essentially become uniformly distributed
on a disc for large n. This is a variant of Girko's Circular law.
Also the asymptotic distribution of random symmetric matrices
is knonw. Since the eigenvalues are real, this gives a distribution on
the line which is called Wigners Semicircle law.
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