Fluctuations of Interlacing Sequences
In a series of works published in the 1990s, Kerov put forth various applications of the circle of ideas centered at the Markov moment problem to the limiting shape of random continual diagrams arising in representation theory and spectral theory. We demonstrate on several examples that his approach...
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| Дата: | 2017 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2017
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| Назва видання: | Журнал математической физики, анализа, геометрии |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/140582 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Fluctuations of Interlacing Sequences / S. Sodin // Журнал математической физики, анализа, геометрии. — 2017. — Т. 13, № 4. — С. 63. — Бібліогр.: 63 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1405822018-07-11T01:23:40Z Fluctuations of Interlacing Sequences Sodin, S. In a series of works published in the 1990s, Kerov put forth various applications of the circle of ideas centered at the Markov moment problem to the limiting shape of random continual diagrams arising in representation theory and spectral theory. We demonstrate on several examples that his approach is also adequate to study the fluctuations about the limiting shape. In the random matrix setting, we compare two continual diagrams: one is constructed from the eigenvalues of the matrix and the critical points of its characteristic polynomial, whereas the second one is constructed from the eigenvalues of the matrix and those of its principal submatrix. The fluctuations of the latter diagram were recently studied by Erd}os and Schröder; we discuss the uctuations of the former, and compare the two limiting processes. For Plancherel random partitions, the Markov correspondence establishes the equivalence between Kerov's central limit theorem for the Young diagram and the Ivanov-Olshanski central limit theorem for the transition measure. We outline a combinatorial proof of the latter, and compare the limiting process with the ones of random matrices. 2017 Article Fluctuations of Interlacing Sequences / S. Sodin // Журнал математической физики, анализа, геометрии. — 2017. — Т. 13, № 4. — С. 63. — Бібліогр.: 63 назв. — англ. 1812-9471 DOI: doi.org/10.15407/mag13.04.364 Mathematics Subject Classification 2000: 60B20, 34L20, 05E10, 60F05, 44A60 http://dspace.nbuv.gov.ua/handle/123456789/140582 en Журнал математической физики, анализа, геометрии Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
In a series of works published in the 1990s, Kerov put forth various applications of the circle of ideas centered at the Markov moment problem to the limiting shape of random continual diagrams arising in representation theory and spectral theory. We demonstrate on several examples that his approach is also adequate to study the fluctuations about the limiting shape. In the random matrix setting, we compare two continual diagrams: one is constructed from the eigenvalues of the matrix and the critical points of its characteristic polynomial, whereas the second one is constructed from the eigenvalues of the matrix and those of its principal submatrix. The fluctuations of the latter diagram were recently studied by Erd}os and Schröder; we discuss the uctuations of the former, and compare the two limiting processes. For Plancherel random partitions, the Markov correspondence establishes the equivalence between Kerov's central limit theorem for the Young diagram and the Ivanov-Olshanski central limit theorem for the transition measure. We outline a combinatorial proof of the latter, and compare the limiting process with the ones of random matrices. |
| format |
Article |
| author |
Sodin, S. |
| spellingShingle |
Sodin, S. Fluctuations of Interlacing Sequences Журнал математической физики, анализа, геометрии |
| author_facet |
Sodin, S. |
| author_sort |
Sodin, S. |
| title |
Fluctuations of Interlacing Sequences |
| title_short |
Fluctuations of Interlacing Sequences |
| title_full |
Fluctuations of Interlacing Sequences |
| title_fullStr |
Fluctuations of Interlacing Sequences |
| title_full_unstemmed |
Fluctuations of Interlacing Sequences |
| title_sort |
fluctuations of interlacing sequences |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2017 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/140582 |
| citation_txt |
Fluctuations of Interlacing Sequences / S. Sodin // Журнал математической физики, анализа, геометрии. — 2017. — Т. 13, № 4. — С. 63. — Бібліогр.: 63 назв. — англ. |
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Журнал математической физики, анализа, геометрии |
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AT sodins fluctuationsofinterlacingsequences |
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2023-10-18T21:22:59Z |
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2023-10-18T21:22:59Z |
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1796152664797478912 |