Wigner Semicircle Distribution

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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 ¿ = ß = 3/2, then X = 2RY - R has the above Wigner semicircle distribution.

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