Integrable operators and the squares of Hankel operators

TL;DR

This paper establishes conditions under which integrable operators, important in random matrix theory, can be expressed as squares of Hankel operators, with applications to special functions like Airy and Whittaker.

Contribution

It provides new sufficient conditions for integrable operators to be represented as squares of Hankel operators, expanding understanding in random matrix theory.

Findings

Conditions for integrable operators to be squares of Hankel operators

Application to Airy, Laguerre, Bessel, and Whittaker functions

Enhanced understanding of eigenvalue distributions in random matrices

Abstract

Integrable operators arise in random matrix theory, where they describe the asymptotic eigenvalue distributions of large self-adjoint random matrices from the generalized unitary ensembles. This paper gives sufficient conditions for an integrable operator to be the square of a Hankel operator, and applies the condition to the Airy, associated Laguerre, modified Besses and Whittaker functions.