Bulk Universality for Unitary Matrix Models
A proof of universality in the bulk of spectrum of unitary matrix models, assuming that the potential is globally C² and locally C³ 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. Th...
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| Datum: | 2009 |
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| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2009
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| Schriftenreihe: | Журнал математической физики, анализа, геометрии |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Bulk Universality for Unitary Matrix Models / M. Poplavskyi // Журнал математической физики, анализа, геометрии. — 2009. — Т. 5, № 3. — С. 245-274. — Бібліогр.: 10 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | A proof of universality in the bulk of spectrum of unitary matrix models, assuming that the potential is globally C² and locally C³ 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. |
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