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.
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More From: Journal of Physics A: Mathematical and Theoretical
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