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math-ph2024
Power spectra of Dyson's circular ensembles
Peter J. Forrester, Nicholas S. Witte
The power spectrum is a Fourier series statistic associated with the covariances of the displacement from average positions of the members of an eigen-sequence. When this eigen-seq…
math-ph2002
Application of the -function theory of Painlevé equations to random matrices: \PV, \PIII, the LUE, JUE and CUE
P. J. Forrester, N. S. Witte
With denoting an average with respect to the eigenvalue PDF for the Laguerre unitary ensemble, the object of our study is $ \tilde{E}_N(I;a,μ) := < \prod_{l=1}^N χ_{(0,\i…