Universality at the Edge for Unitary Matrix Models
Using the results on the 1/n-expansion of the Verblunsky coe±cients 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 pr...
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| Date: | 2012 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2012
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| Series: | Журнал математической физики, анализа, геометрии |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/106729 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Universality at the Edge for Unitary Matrix Models / M. Poplavskyi // Журнал математической физики, анализа, геометрии. — 2012. — Т. 8, № 4. — С. 367-392. — Бібліогр.: 17 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | Using the results on the 1/n-expansion of the Verblunsky coe±cients 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 di®erentiable potentials and of supports, consisting of one interval. |
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