The Wigner's semicircle distribution  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.
 Wigner, E. "Characteristic Vectors of Bordered Matrices with Infinite Dimensions." Ann. of Math. 62, 548-564, 1955.
Youssef Khmou (2022). Wigner's Semicircle Law (https://www.mathworks.com/matlabcentral/fileexchange/46464-wigner-s-semicircle-law), MATLAB Central File Exchange. Retrieved .
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