The above ar plots of the scaled level densities of the Gaussian orthogonal ensemble of random matrices (beta = 2) of sizes n = 4,6,8, and 10.  They are plotted against the scaled semicircle, which is the limiting distribution as n goes to infinity. Notice the "bumps" in each picture! There are exactly as many as the matrix size.



Now observe the level densities above; they correspond to the size 4 Hermite ensembles of beta = 2 through 10. The size of the 4 "bumps" increases with beta. The smallest-bumped graph also appears in the subwindow 1 above. Can you guess what happens as we let beta go to infinity? The answer is appears below in background-colored ink (highlight it to read it).

The limiting distribution is the average of 4 Delta Dirac distributions. Care to guess the supports? =)

The plot above was obtained with MOPs.