4 citations · 4 across the 4 of their papers we have counts for
9 papers
Bi-orthogonal Polynomials on the Unit Circle, regular semi-classical Weights and Integrable Systems
P. J. Forrester, N. S. Witte
The theory of bi-orthogonal polynomials on the unit circle is developed for a general class of weights leading to systems of recurrence relations and derivatives of the polynomials…
Discrete Painlevé equations, Orthogonal Polynomials on the Unit Circle and -recurrences for averages over U(N) -- \PVI -functions
P. J. Forrester, N. S. Witte
The theory of orthogonal polynomials on the unit circle is developed for a general class of weights leading to systems of recurrence relations and derivatives of the polynomials an…
Discrete Painlevé equations, Orthogonal Polynomials on the Unit Circle and N-recurrences for averages over U(N) -- \PIIIa and \PV -functions
P. J. Forrester, N. S. Witte
In this work we show that the Toeplitz determinants with the symbols and -- known -functions for th…
New Transformations for Painlevé's Third Transcendent
N. S. Witte
We present transformations relating the third transcendent of Painlevé with parameter sets located at the corners of the Weyl chamber for the symmetry group of the system, the affi…
Discriminants and Functional Equations for Polynomials Orthogonal on the Unit Circle
Mourad E. H. Ismail, Nicholas S. Witte
We derive raising and lowering operators for orthogonal polynomials on the unit circle and find second order differential and -difference equations for these polynomials. A gene…
Exact Wigner surmise type evaluation of the spacing distribution in the bulk of the scaled random matrix ensembles
P. J. Forrester, N. S. Witte
Random matrix ensembles with orthogonal and unitary symmetry correspond to the cases of real symmetric and Hermitian random matrices respectively. We show that the probability dens…