The eigenvalue probability density function (PDF) for the Gaussian unitary ensemble has a
well-known analogy with the Boltzmann factor for a classical log-gas with pair potential− log …

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 …

We outline a relation between the densities for the β-ensembles with respect to the Jacobi
weight (1− x) a (1+ x) b supported on the interval (− 1, 1) and the Cauchy weight (1− ix) η (1+ …

The generalisation of continuous orthogonal polynomial ensembles from random matrix
theory to the q-lattice setting is considered. We take up the task of initiating a systematic …

There is a two-component log-gas system with Boltzmann factor which provides an
interpolation between the eigenvalue probability density function (PDF) for β= 1 and β= 4 …

We consider series over Young diagrams of products of Schur functions $ s_
{\lambda\cup\lambda} $, marked with``fat partitions''$\lambda\cup\lambda $, which appear in …

Inspired by Aomoto's q-Selberg integral, a study is made of an orthogonal ensemble on an
exponential lattice. By introducing a skew symmetric kernel, the configuration space of this …

This paper is to evaluate certain Catalan-Hankel Pfaffians by the theory of skew orthogonal
polynomials. Due to different kinds of hypergeometric orthogonal polynomials underlying the …

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

Particular class of skew orthogonal polynomials are introduced and investigated, which
possess Laurent symmetry. They are also shown to appear as eigenfunctions of symplectic …