Tracy and Widom have evaluated the cumulative distribution of the largest eigenvalue for the finite and scaled infinite GUE in terms of a PIV and PII transcendent respectively. We generalise theseâ€¦ (More)

The probabilities for gaps in the eigenvalue spectrum of finite N Ã—N random unitary ensembles on the unit circle with a singular weight, and the related Hermitian ensembles on the line with Cauchyâ€¦ (More)

We derive raising and lowering operators for orthogonal polynomials on the unit circle and find second order differential and q-difference equations for these polynomials. A general functionalâ€¦ (More)

A feature of certain ensembles of random matrices is that the corresponding measure is invariant under conjugation by unitary matrices. Study of such ensembles realised by matrices with Gaussianâ€¦ (More)

P.J. Forrester and N.S. Witteâ€ Department of Mathematics and Statistics â€ (and School of Physics), University of Melbourne, Victoria 3010, Australia email: p.forrester@ms.unimelb.edu.au;â€¦ (More)

The loop equation formalism is used to compute the 1/N expansion of the resolvent for the Gaussian Î² ensemble up to and including the term at O(Nâˆ’6). This allows the moments of the eigenvalue densityâ€¦ (More)

We consider the physical combinatorics of critical lattice models and their associated conformal field theories arising in the continuum scaling limit. As examples, we consider A-type unitary minimalâ€¦ (More)

In a previous work a random matrix average for the Laguerre unitary ensemble, generalising the generating function for the probability that an interval (0, s) at the hard edge contains k eigenvalues,â€¦ (More)