On the Scaling Limits of Determinantal Point Processes with Kernels Induced by Sturm-Liouville Operators
By applying an idea of Borodin and Olshanski [J. Algebra 313 (2007), 40-60], we study various scaling limits of determinantal point processes with trace class projection kernels given by spectral projections of selfadjoint Sturm-Liouville operators. Instead of studying the convergence of the kernels...
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| Дата: | 2016 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2016
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147850 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | On the Scaling Limits of Determinantal Point Processes with Kernels Induced by Sturm-Liouville Operators / F. Bornemann // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 25 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1478502019-02-17T01:27:19Z On the Scaling Limits of Determinantal Point Processes with Kernels Induced by Sturm-Liouville Operators Bornemann, F. By applying an idea of Borodin and Olshanski [J. Algebra 313 (2007), 40-60], we study various scaling limits of determinantal point processes with trace class projection kernels given by spectral projections of selfadjoint Sturm-Liouville operators. Instead of studying the convergence of the kernels as functions, the method directly addresses the strong convergence of the induced integral operators. We show that, for this notion of convergence, the Dyson, Airy, and Bessel kernels are universal in the bulk, soft-edge, and hard-edge scaling limits. This result allows us to give a short and unified derivation of the known formulae for the scaling limits of the classical random matrix ensembles with unitary invariance, that is, the Gaussian unitary ensemble (GUE), the Wishart or Laguerre unitary ensemble (LUE), and the MANOVA (multivariate analysis of variance) or Jacobi unitary ensemble (JUE). 2016 Article On the Scaling Limits of Determinantal Point Processes with Kernels Induced by Sturm-Liouville Operators / F. Bornemann // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 25 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 15B52; 34B24; 33C45 DOI:10.3842/SIGMA.2016.083 http://dspace.nbuv.gov.ua/handle/123456789/147850 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
By applying an idea of Borodin and Olshanski [J. Algebra 313 (2007), 40-60], we study various scaling limits of determinantal point processes with trace class projection kernels given by spectral projections of selfadjoint Sturm-Liouville operators. Instead of studying the convergence of the kernels as functions, the method directly addresses the strong convergence of the induced integral operators. We show that, for this notion of convergence, the Dyson, Airy, and Bessel kernels are universal in the bulk, soft-edge, and hard-edge scaling limits. This result allows us to give a short and unified derivation of the known formulae for the scaling limits of the classical random matrix ensembles with unitary invariance, that is, the Gaussian unitary ensemble (GUE), the Wishart or Laguerre unitary ensemble (LUE), and the MANOVA (multivariate analysis of variance) or Jacobi unitary ensemble (JUE). |
| format |
Article |
| author |
Bornemann, F. |
| spellingShingle |
Bornemann, F. On the Scaling Limits of Determinantal Point Processes with Kernels Induced by Sturm-Liouville Operators Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Bornemann, F. |
| author_sort |
Bornemann, F. |
| title |
On the Scaling Limits of Determinantal Point Processes with Kernels Induced by Sturm-Liouville Operators |
| title_short |
On the Scaling Limits of Determinantal Point Processes with Kernels Induced by Sturm-Liouville Operators |
| title_full |
On the Scaling Limits of Determinantal Point Processes with Kernels Induced by Sturm-Liouville Operators |
| title_fullStr |
On the Scaling Limits of Determinantal Point Processes with Kernels Induced by Sturm-Liouville Operators |
| title_full_unstemmed |
On the Scaling Limits of Determinantal Point Processes with Kernels Induced by Sturm-Liouville Operators |
| title_sort |
on the scaling limits of determinantal point processes with kernels induced by sturm-liouville operators |
| publisher |
Інститут математики НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147850 |
| citation_txt |
On the Scaling Limits of Determinantal Point Processes with Kernels Induced by Sturm-Liouville Operators / F. Bornemann // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 25 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2023-05-20T17:28:40Z |
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2023-05-20T17:28:40Z |
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