From gap probabilities in random matrix theory to eigenvalue expansions*
Year: 2016
Type: article
Abstract: We present a method to derive asymptotics of eigenvalues for trace-class integral operators , acting on a single interval , which belongs to the ring of integrable operators (Its et al 1990 Int. J. Mod. Phys. B 4 1003–37 ). Our emphasis lies on the behavior of the spectrum of K as and i is fixed. We show that this behavior is intimately linked to the analysis of the Fredholm determinant as and in a Stokes type scaling regime. Concrete asymptotic formulæ are obtained for the eigenvalues of Airy and Bessel kernels in random matrix theory.
Author: Thomas Bothner
Institution: University of Michigan
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2196311583