Recurrence coefficients of semi-classical orthogonal polynomials (orthogonal polynomials
related to a weight function w such that w′ w is a rational function) are shown to be …

Symmetries of the infinite Toda lattice. The symmetries for the infinite Toda lattice,(oi)%
t=[\{Ln)» L]> η= 1> 2>···> viewed as isospectral deformations of bi-infinite tri diagonal …

In this paper we study the simplest deformation on a sequence of orthogonal polynomials.
This in turn induces a deformation on the moment matrix of the polynomials and associated …

On the one hand the work of R. Askey and J. Wilson [3] shows that if one enters the “land of
g” and replaces derivatives by q-derivatives then one gets a much larger class of …

We consider orthogonal polynomials pn with respect to an exponential weight function w
(x)= exp (-P (x)). The related equations for the recurrence coefficients have been explored by …

Applying the Coulomb fluid approach to the Hermitian random matrix ensembles, universal
derivatives of the free energy for a system of N logarithmically repelling classical particles …

We show that maximal rank 1 commutative rings of difference operators can be
systematically constructed from their differential analogues by making an appropriate shift in …

We consider the Laguerre partition function and derive explicit generating functions for
connected correlators with arbitrary integer powers of traces in terms of products of Hahn …

We give a new proof of the equivalence between the dessin partition function and the
partition function of the Laguerre unitary ensemble (LUE), originally found by Ambjørn and …

The six Painlevé transcendants which originally appeared in the studies of ordinary
differential equations have been found numerous applications in physical problems. The …