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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| Veröffentlicht in: | Журнал математической физики, анализа, геометрии |
|---|---|
| Datum: | 2009 |
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| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2009
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/106543 |
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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| _version_ | 1862615180791250944 |
|---|---|
| author | Poplavskyi, M. |
| author_facet | Poplavskyi, M. |
| citation_txt | Bulk Universality for Unitary Matrix Models / M. Poplavskyi // Журнал математической физики, анализа, геометрии. — 2009. — Т. 5, № 3. — С. 245-274. — Бібліогр.: 10 назв. — англ. |
| collection | DSpace DC |
| container_title | Журнал математической физики, анализа, геометрии |
| description | 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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| first_indexed | 2025-11-29T13:07:08Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-106543 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1812-9471 |
| language | English |
| last_indexed | 2025-11-29T13:07:08Z |
| publishDate | 2009 |
| publisher | Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| record_format | dspace |
| spelling | Poplavskyi, M. 2016-09-30T07:29:38Z 2016-09-30T07:29:38Z 2009 Bulk Universality for Unitary Matrix Models / M. Poplavskyi // Журнал математической физики, анализа, геометрии. — 2009. — Т. 5, № 3. — С. 245-274. — Бібліогр.: 10 назв. — англ. 1812-9471 https://nasplib.isofts.kiev.ua/handle/123456789/106543 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. The author is grateful to Dr. M.V. Shcherbina for the problem statement and fruitful discussions. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Журнал математической физики, анализа, геометрии Bulk Universality for Unitary Matrix Models Article published earlier |
| spellingShingle | Bulk Universality for Unitary Matrix Models Poplavskyi, M. |
| title | Bulk Universality for Unitary Matrix Models |
| title_full | Bulk Universality for Unitary Matrix Models |
| title_fullStr | Bulk Universality for Unitary Matrix Models |
| title_full_unstemmed | Bulk Universality for Unitary Matrix Models |
| title_short | Bulk Universality for Unitary Matrix Models |
| title_sort | bulk universality for unitary matrix models |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/106543 |
| work_keys_str_mv | AT poplavskyim bulkuniversalityforunitarymatrixmodels |