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math.CA2000
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…
math-ph2000
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…
math-ph2000
Integrability, Random Matrices and Painlevé Transcendents
N. S. Witte, P. J. Forrester, Christopher M. Cosgrove
The probability that an interval is free of eigenvalues in a matrix ensemble with unitary symmetry is given by a Fredholm determinant. When the weight function in the matrix en…