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1 December 2019 Splitting of a gap in the bulk of the spectrum of random matrices
Benjamin Fahs, Igor Krasovsky
Duke Math. J. 168(18): 3529-3590 (1 December 2019). DOI: 10.1215/00127094-2019-0036

Abstract

We consider the probability of having two intervals (gaps) without eigenvalues in the bulk scaling limit of the Gaussian unitary ensemble of random matrices. We describe uniform asymptotics for the transition between a single large gap and two large gaps. For the initial stage of the transition, we explicitly determine all the asymptotic terms (up to the decreasing ones) of the logarithm of the probability. We obtain our results by analyzing double-scaling asymptotics of a Toeplitz determinant whose symbol is supported on two arcs of the unit circle.

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Benjamin Fahs. Igor Krasovsky. "Splitting of a gap in the bulk of the spectrum of random matrices." Duke Math. J. 168 (18) 3529 - 3590, 1 December 2019. https://doi.org/10.1215/00127094-2019-0036

Information

Received: 18 August 2017; Revised: 14 May 2019; Published: 1 December 2019
First available in Project Euclid: 7 November 2019

zbMATH: 07174393
MathSciNet: MR4034892
Digital Object Identifier: 10.1215/00127094-2019-0036

Subjects:
Primary: 60B20
Secondary: 47B35

Keywords: asymptotic analysis , Random matrix theory , Toeplitz determinants

Rights: Copyright © 2019 Duke University Press

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Vol.168 • No. 18 • 1 December 2019
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