193 citations · 2.8k across the 159 of their papers we have counts for
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Singular Values of Products of Ginibre Random Matrices
N. S. Witte, P. J. Forrester
The squared singular values of the product of complex Ginibre matrices form a biorthogonal ensemble, and thus their distribution is fully determined by a correlation kernel. Th…
Joint distribution of the first and second eigenvalues at the soft edge of unitary ensembles
N. S. Witte, F. Bornemann, P. J. Forrester
The density function for the joint distribution of the first and second eigenvalues at the soft edge of unitary ensembles is found in terms of a Painlevé II transcendent and its as…
On the Variance of the Index for the Gaussian Unitary Ensemble
N. S. Witte, P. J. Forrester
We derive simple linear, inhomogeneous recurrences for the variance of the index by utilising the fact that the generating function for the distribution of the number of positive e…
Fredholm Determinant evaluations of the Ising Model diagonal correlations and their λ- generalisation
N. S. Witte, P. J. Forrester
The diagonal spin-spin correlations of the square lattice Ising model, originally expressed as Toeplitz determinants, are given by two distinct Fredholm determinants - one with an…
Differential equations for deformed Laguerre polynomials
Peter J. Forrester, Christopher M. Ormerod
The distribution function for the first eigenvalue spacing in the Laguerre unitary ensemble of finite size may be expressed in terms of a solution of the fifth Painleve transcenden…
The importance of the Selberg integral
Peter J. Forrester, S. Ole Warnaar
It has been remarked that a fair measure of the impact of Atle Selberg's work is the number of mathematical terms which bear his name. One of these is the Selberg integral, an n-di…