Nicholas S. Witte

collaborators

3 papers

math.CA2026

The $2 j - k$ and $j - 2 k$ Bi-orthogonal Polynomials on the Unit Circle: Further Properties and Riemann-Hilbert Characterizations

Roozbeh Gharakhloo, Nicholas S. Witte

In previous work \cite{GW}, we developed a theory of modulated $2j-k$ bi-orthogonal polynomial systems $\{P_n(z;r),Q_n(z;r)\}$ and $j-2k$ bi-orthogonal polynomial systems \(\…

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 $τ$ -function theory of Painlevé equations to random matrices: \PV, \PIII, the LUE, JUE and CUE

P. J. Forrester, N. S. Witte

With $< \cdot >$ 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…

The 2j−k and j−2k Bi-orthogonal Polynomials on the Unit Circle: Further Properties and Riemann-Hilbert Characterizations

Power spectra of Dyson's circular ensembles

Application of the τ-function theory of Painlevé equations to random matrices: \PV, \PIII, the LUE, JUE and CUE

The $2 j - k$ and $j - 2 k$ Bi-orthogonal Polynomials on the Unit Circle: Further Properties and Riemann-Hilbert Characterizations

Application of the $τ$ -function theory of Painlevé equations to random matrices: \PV, \PIII, the LUE, JUE and CUE