Discrete Tracy--Widom operators.

Blower, Gordon and McCafferty, Andrew (2009) Discrete Tracy--Widom operators. Proceedings of the Edinburgh Mathematical Society, 52 (3). pp. 545-559. ISSN 1464-3839

Abstract

Integrable operators arise in random matrix theory, where they describe the asymptotic eigenvalue distribution of large self-adjoint random matrices from the generalized unitary ensembles. This paper considers discrete Tracy--Widom operators, and gives sufficient conditions for a discrete integrable operator to be the square of a Hankel matrix. Examples include the discrete Bessel kernel and kernels arising from the almost Mathieu equatio and the Fourier transform of Mathieu's equation.