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 …

We establish the asymptotic expansion in $\beta $ matrix models with a confining, off-critical
potential in the regime where the support of the equilibrium measure is a finite union of …

Given the Hermitian, symmetric and symplectic ensembles, it is shown that the probability
that the spectrum belongs to one or several intervals satisfies a nonlinear PDE. This is done …

Skew-orthogonal polynomials (SOPs) arise in the study of the n-point distribution function for
orthogonal and symplectic random matrix ensembles. Motivated by the average of …

Non-Hermitian random matrices with symplectic symmetry provide examples for Pfaffian
point processes in the complex plane. These point processes are characterised by a matrix …

This paper focuses on different reductions of the two-dimensional (2d)-Toda hierarchy.
Symmetric and skew-symmetric moment matrices are first considered, resulting in differential …

The Pfaff lattice was introduced by us in the context of a Lie algebra splitting of \rmgl(∞) into
\rmsp(∞) and an algebra of lower-triangular matrices. The Pfaff lattice is equivalent to a set …

We obtain the collection of symmetric and symplectic matrix integrals and the collection of
Pfaffian tau-functions, recently described by Peng and Adler and van Moerbeke, as specific …

We show that the Riemannian Gaussian distributions on symmetric spaces, introduced in
recent years, are of standard random matrix type. We exploit this to compute analytically …

Motivated by the Novikov equation and its peakon problem, we propose a new mixed type
Hermite–Padé approximation whose unique solution is a sequence of polynomials …