Discrete orthogonal ensemble on the exponential lattices

Abstract

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 ensemble is constructed to be symmetric and thus the corresponding skew inner product, skew orthogonal polynomials as well as correlation functions are explicitly formulated. These involve polynomials from the Askey scheme. Examples considered include the Al-Salam & Carlitz, q-Laguerre, little q-Jacobi and big q-Jacobi cases.