Studying the Asymptotics of Selberg-Type Integrals

Abstract

This paper presents an argument in favor of the analysis of a certain integral, which we like to call a “Selberg-Type Integral.” We wish first to show how this integral has come to be involved in a rather bewildering variety of mathematical and physical theories, including the theory of random matrices, the theory of CalogeroSutherland models, the Fractional Quantum Hall effect, the topology of the moduli space of algebraic curves and certain ideas in number theory.