  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 equation and the Fourier
transform of Mathieu's equation.
