On Universality of Bulk Local Regime of the Deformed Gaussian Unitary Ensemble
We consider the deformed Gaussian Ensemble Hn = Hn⁽⁰⁾ +Mn in which Hn⁽⁰⁾ is a hermitian matrix (possibly random) and Mn is the Gaussian Unitary Ensemble (GUE) random matrix (independent of Hn⁽⁰⁾ ). Assuming that the Normalized Counting Measure of Hn⁽⁰⁾converges weakly (in probability) to a nonrandom...
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| Published in: | Журнал математической физики, анализа, геометрии |
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| Date: | 2009 |
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| Format: | Article |
| Language: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2009
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/106551 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On Universality of Bulk Local Regime of the Deformed Gaussian Unitary Ensemble / T. Shcherbina // Журнал математической физики, анализа, геометрии. — 2009. — Т. 5, № 4. — С. 396-433. — Бібліогр.: 16 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862715200806846464 |
|---|---|
| author | Shcherbina, T. |
| author_facet | Shcherbina, T. |
| citation_txt | On Universality of Bulk Local Regime of the Deformed Gaussian Unitary Ensemble / T. Shcherbina // Журнал математической физики, анализа, геометрии. — 2009. — Т. 5, № 4. — С. 396-433. — Бібліогр.: 16 назв. — англ. |
| collection | DSpace DC |
| container_title | Журнал математической физики, анализа, геометрии |
| description | We consider the deformed Gaussian Ensemble Hn = Hn⁽⁰⁾ +Mn in which Hn⁽⁰⁾ is a hermitian matrix (possibly random) and Mn is the Gaussian Unitary Ensemble (GUE) random matrix (independent of Hn⁽⁰⁾ ). Assuming that the Normalized Counting Measure of Hn⁽⁰⁾converges weakly (in probability) to a nonrandom measure N⁽⁰⁾ with a bounded support, we prove the universality of the local eigenvalue statistics in the bulk of the limiting spectrum of Hn.
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| first_indexed | 2025-12-07T17:56:43Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-106551 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1812-9471 |
| language | English |
| last_indexed | 2025-12-07T17:56:43Z |
| publishDate | 2009 |
| publisher | Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| record_format | dspace |
| spelling | Shcherbina, T. 2016-09-30T08:25:42Z 2016-09-30T08:25:42Z 2009 On Universality of Bulk Local Regime of the Deformed Gaussian Unitary Ensemble / T. Shcherbina // Журнал математической физики, анализа, геометрии. — 2009. — Т. 5, № 4. — С. 396-433. — Бібліогр.: 16 назв. — англ. 1812-9471 https://nasplib.isofts.kiev.ua/handle/123456789/106551 We consider the deformed Gaussian Ensemble Hn = Hn⁽⁰⁾ +Mn in which Hn⁽⁰⁾ is a hermitian matrix (possibly random) and Mn is the Gaussian Unitary Ensemble (GUE) random matrix (independent of Hn⁽⁰⁾ ). Assuming that the Normalized Counting Measure of Hn⁽⁰⁾converges weakly (in probability) to a nonrandom measure N⁽⁰⁾ with a bounded support, we prove the universality of the local eigenvalue statistics in the bulk of the limiting spectrum of Hn. The author is grateful to Prof. L. Pastur for many interesting discussions of the problem. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Журнал математической физики, анализа, геометрии On Universality of Bulk Local Regime of the Deformed Gaussian Unitary Ensemble Article published earlier |
| spellingShingle | On Universality of Bulk Local Regime of the Deformed Gaussian Unitary Ensemble Shcherbina, T. |
| title | On Universality of Bulk Local Regime of the Deformed Gaussian Unitary Ensemble |
| title_full | On Universality of Bulk Local Regime of the Deformed Gaussian Unitary Ensemble |
| title_fullStr | On Universality of Bulk Local Regime of the Deformed Gaussian Unitary Ensemble |
| title_full_unstemmed | On Universality of Bulk Local Regime of the Deformed Gaussian Unitary Ensemble |
| title_short | On Universality of Bulk Local Regime of the Deformed Gaussian Unitary Ensemble |
| title_sort | on universality of bulk local regime of the deformed gaussian unitary ensemble |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/106551 |
| work_keys_str_mv | AT shcherbinat onuniversalityofbulklocalregimeofthedeformedgaussianunitaryensemble |