Abstract
The probability density function of the single eigenvalue is expanded in terms of the reciprocal of the dimension of the matrix using Bessel functons. It is shown that for the new matrix ensembles this expansion gives Wigner's semicircle centered at the mean value of the matrix elements plus terms of the order ofN −1, whereN is the dimension of the matrix.
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Ullah, N. On the expansion of the single eigenvalue probability density function. J Stat Phys 24, 413–418 (1981). https://doi.org/10.1007/BF01012813
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DOI: https://doi.org/10.1007/BF01012813