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Zhurnal Matematicheskoi Fiziki, Analiza, Geometrii [Journal of Mathematical Physics, Analysis, Geometry], 2012, Volume 8, Number 4, Pages 367–392
(Mi jmag543)
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Universality at the edge for unitary matrix models
M. Poplavskyi Mathematics Division, B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, 47 Lenin Ave., Kharkiv, 61103, Ukraine
Abstract:
Using the results on the $1/n$-expansion of the Verblunsky coefficients for a class of polynomials orthogonal on the unit circle with $n$ varying weight, we prove that the local eigenvalue statistic for unitary matrix models is
independent of the form of the potential, determining the matrix model. Our proof is applicable to the case of four times differentiable potentials and of supports, consisting of one interval.
Key words and phrases:
unitary matrix models, local eigenvalue statistics, universality, polynomials orthogonal on the unit circle.
Received: 05.08.2012
Citation:
M. Poplavskyi, “Universality at the edge for unitary matrix models”, Zh. Mat. Fiz. Anal. Geom., 8:4 (2012), 367–392
Linking options:
https://www.mathnet.ru/eng/jmag543 https://www.mathnet.ru/eng/jmag/v8/i4/p367
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Abstract page: | 128 | Full-text PDF : | 41 | References: | 32 |
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