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Zhurnal Matematicheskoi Fiziki, Analiza, Geometrii [Journal of Mathematical Physics, Analysis, Geometry], 2009, Volume 5, Number 3, Pages 245–274
(Mi jmag127)
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This article is cited in 2 scientific papers (total in 2 papers)
Bulk universality for unitary matrix models
M. Poplavskyi Mathematical Division, B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, 47 Lenin Ave., Kharkiv, 61103, Ukraine
Abstract:
A proof of universality in the bulk of spectrum of unitary matrix models, assuming that the potential is globally $C^2$ and locally $C^3$ function (see Theorem 1.2), is given. The proof is based on the determinant formulas for correlation functions in terms of polynomials orthogonal on the unit circle. The sin-kernel is obtained as a unique solution of a certain nonlinear integrodifferential equation without using asymptotics of orthogonal polynomials.
Key words and phrases:
unitary matrix models, local eigenvalue statistics, universality.
Received: 25.04.2008
Citation:
M. Poplavskyi, “Bulk universality for unitary matrix models”, Zh. Mat. Fiz. Anal. Geom., 5:3 (2009), 245–274
Linking options:
https://www.mathnet.ru/eng/jmag127 https://www.mathnet.ru/eng/jmag/v5/i3/p245
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Abstract page: | 163 | Full-text PDF : | 42 | References: | 36 |
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