Integrable operators and the squares of Hankel operators

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.

14 pages

References in corpus (2)

• Asymptotics of Plancherel-type random partitions
• Integrable operators and squares of Hankel Matrices

Cited by in corpus (6)

• Hankel operators that commute with second-order differential operators
• On tau functions for orthogonal polynomials and matrix models
• Discrete Tracy-Widom Operators
• Kernels and point processes associated with Whittaker functions
• On linear systems and tau functions associated with Lame's equation and Painleve's equation VI
• Linear systems and determinantal random point fields