On the Scaling Limits of Determinantal Point Processes with Kernels Induced by Sturm-Liouville Operators
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
On the Scaling Limits of Determinantal Point Processes with Kernels Induced by Sturm-Liouville Operators
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| Creator |
Bornemann, F.
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| 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).
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| Date |
2019-02-16T09:16:49Z
2019-02-16T09:16:49Z 2016 |
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| Type |
Article
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| Identifier |
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 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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