Wigner's Semicircle Law

Wigner's semicircle law : modelling the distribution of the eigenvalues of symmetric random matrix.


Updated 6 May 2014

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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.

Cite As

Youssef Khmou (2023). Wigner's Semicircle Law (https://www.mathworks.com/matlabcentral/fileexchange/46464-wigner-s-semicircle-law), MATLAB Central File Exchange. Retrieved .

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