Correlations for the orthogonal-unitary and symplectic-unitary transitions at the hard and soft edges Abstract For the orthogonal-unitary and symplectic-unitary transitions in random matrix theory ,… (More)

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 these… (More)

The probabilities for gaps in the eigenvalue spectrum of finite N ×N random unitary ensembles on the unit circle with a singular weight, and the related Hermitian ensembles on the line with Cauchy… (More)

Skew orthogonal polynomials arise in the calculation of the n-point distribution function for the eigenvalues of ensembles of random matrices with orthogonal or symplectic symmetry. In particular,… (More)

In (1.2) mκ(z) is the monomial symmetric function in the variables z1, . . . , zN , and the sum is over all partitions μ which have the same modulus as κ but are smaller in dominance ordering. The… (More)

The circular and Jacobi ensembles of random matrices have their eigenvalue support on the unit circle of the complex plane and the interval (0, 1) of the real line respectively. The averaged value of… (More)

A q-analogue of the type A Dunkl operator and integral kernel We introduce the q-analogue of the type A Dunkl operators, which are a set of degree–lowering operators on the space of polynomials in n… (More)