Random matrix theory, both as an application and as a theory, has evolved rapidly over the past fifteen years. Log-Gases and Random Matrices gives a comprehensive account of these developments,… Expand

AbstractThe eight-vertex model is equivalent to a “solid-on-solid” (SOS) model, in which an integer heightli is associated with each sitei of the square lattice. The Boltzmann weights of the model… Expand

Abstract:Multivariable generalizations of the classical Hermite, Laguerre and Jacobi polynomials occur as the polynomial part of the eigenfunctions of certain Schrödinger operators for… Expand

It has been remarked that a fair measure of the impact of Atle Selberg’s work is the number of mathematical terms that bear his name. One of these is the Selberg integral, an n-dimensional… Expand

The restricted eight-vertex solid-on-solid (SOS) model is an exactly solvable class of two-dimensional lattice models. To each sitei of the lattice there is associated an integer heightli restricted… Expand

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 $n$ variables. This allows the construction of… Expand

A computationally tractable formula for the cumulative probability density of the largest real eigenvalue is presented, relevant to May's stability analysis of biological webs.Expand