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High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! The Wigner semicircle distribution, named after the physicist Eugene Wigner, is the probability distribution supported on the interval [ R, R] the graph of whose probability density function f is a semicircle of radius R centered at (0, 0) and then suitably normalized (so that it is really a semi-ellipse). This distribution arises as the limiting distribution of eigenvalues of many random symmetric matrices as the size of the matrix approaches infinity. It is a scaled beta distribution, more precisely, if Y is beta distributed with parameters = = 3/2, then X = 2RY R has the above Wigner semicircle distribution.