Universality of the matrix Airy and Bessel functions at spectral edges of unitary ensembles

Abstract

This paper deals with products and ratios of average characteristic polynomials for unitary ensembles. We prove universality at the soft edge of the limiting eigenvalues' density, and write the universal limit in function of the Kontsevich matrix model ("matrix Airy function", as originally named by Kontsevich). For the case of the hard edge, universality is already known. We show that also in this case the universal limit can be expressed as a matrix integral ("matrix Bessel function") known in the literature as generalized Kontsevich matrix model.

20 pages, 1 figure

References in corpus (1)

• The Kontsevich matrix integral: convergence to the Painlevé hierarchy and Stokes' phenomenon

Cited by in corpus (2)

• JT gravity, KdV equations and macroscopic loop operators
• Matrix models for stationary Gromov-Witten invariants of the Riemann sphere