Eigenvalue distributions of random permutation matrices

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Logarithmic Combinatorial Structures: A Probabilistic Approach (2003, background): “Connections between the eigenvalues of a random permutation matrix (which are determined by the cycle structure of the permutation), the eigenvalues of a random unitary matrix and the Riemann zeta function are uncovered by Wieand (1998, 2000) and Hambly et al. (1999).”
New tests of the correspondence between unitary eigenvalues and the zeros of Riemann's zeta function (2000, background): “Wieand [59] has proved that for large n, a random element of Sn has eigenvalues which obey the limiting normal distribution with correlations given by theorem 3.”
PATTERNS IN EIGENVALUES: THE 70TH JOSIAH WILLARD GIBBS LECTURE (2003, methodology): “A second test may be based on strange correlations found by Kelly Wieand [96], [97].”
Patterns in eigenvalues: the 70th Josiah Willard Gibbs lecture (2003, methodology): “A second test may be based on strange correlations found by Kelly Wieand [96], [97].”