Wigner's Semicircle Law

The Wigner's semicircle distribution [1] is law that was observed in 1955 while studying The Hamiltonian operator in quantum mechanics.
This law describes the distribution of the eigenvalues of certain symmetric random matrices when the dimension N tends to infinity.
In this tutorial, we take an example of symmetric random matrix M drawn from normal distribution with dimension N=1000.
The theoretical and numerical Probability density functions of M are illustrated.
[1] Wigner, E. "Characteristic Vectors of Bordered Matrices with Infinite Dimensions." Ann. of Math. 62, 548-564, 1955.