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): for −R ≤ x ≤ R, and f(x) = 0 if R < |x|. This distribution arises as the limiting distribution of eigenvalues of many random symmetric matrices as the size of the matrix approaches infinity.