Spherical Induced Ensembles with Symplectic Symmetry
We consider the complex eigenvalues of the induced spherical Ginibre ensemble with symplectic symmetry and establish the local universality of these point processes along the real axis. We derive scaling limits of all correlation functions at regular points, both in the strong and weak non-unitary r...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2023 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2023
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211910 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Spherical Induced Ensembles with Symplectic Symmetry. Sung-Soo Byun and Peter J. Forrester. SIGMA 19 (2023), 033, 28 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862725114240434176 |
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| author | Byun, Sung-Soo Forrester, Peter J. |
| author_facet | Byun, Sung-Soo Forrester, Peter J. |
| citation_txt | Spherical Induced Ensembles with Symplectic Symmetry. Sung-Soo Byun and Peter J. Forrester. SIGMA 19 (2023), 033, 28 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We consider the complex eigenvalues of the induced spherical Ginibre ensemble with symplectic symmetry and establish the local universality of these point processes along the real axis. We derive scaling limits of all correlation functions at regular points, both in the strong and weak non-unitary regimes, as well as at the origin, having a spectral singularity. A key ingredient of our proof is a derivation of a differential equation satisfied by the correlation kernels of the associated Pfaffian point processes, thereby allowing us to perform asymptotic analysis.
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| first_indexed | 2026-03-21T08:03:02Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211910 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T08:03:02Z |
| publishDate | 2023 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Byun, Sung-Soo Forrester, Peter J. 2026-01-16T11:17:25Z 2023 Spherical Induced Ensembles with Symplectic Symmetry. Sung-Soo Byun and Peter J. Forrester. SIGMA 19 (2023), 033, 28 pages 1815-0659 2020 Mathematics Subject Classification: 60B20; 33C45; 33E12 arXiv:2209.01934 https://nasplib.isofts.kiev.ua/handle/123456789/211910 https://doi.org/10.3842/SIGMA.2023.033 We consider the complex eigenvalues of the induced spherical Ginibre ensemble with symplectic symmetry and establish the local universality of these point processes along the real axis. We derive scaling limits of all correlation functions at regular points, both in the strong and weak non-unitary regimes, as well as at the origin, having a spectral singularity. A key ingredient of our proof is a derivation of a differential equation satisfied by the correlation kernels of the associated Pfaffian point processes, thereby allowing us to perform asymptotic analysis. The authors thank Markus Ebke for the help with numerical simulations. Sung-Soo Byun was supported by Samsung Science and Technology Foundation (SSTF-BA1401-51), by a KIAS Individual Grant (SP083201) via the Center for Mathematical Challenges at Korea Institute for Advanced Study, by the National Research Foundation of Korea (NRF-2019R1A5A1028324), and by the POSCO TJ Park Foundation (POSCO Science Fellowship). Funding support to Peter Forrester for this research was through the Australian Research Council Discovery Project grant DP210102887. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Spherical Induced Ensembles with Symplectic Symmetry Article published earlier |
| spellingShingle | Spherical Induced Ensembles with Symplectic Symmetry Byun, Sung-Soo Forrester, Peter J. |
| title | Spherical Induced Ensembles with Symplectic Symmetry |
| title_full | Spherical Induced Ensembles with Symplectic Symmetry |
| title_fullStr | Spherical Induced Ensembles with Symplectic Symmetry |
| title_full_unstemmed | Spherical Induced Ensembles with Symplectic Symmetry |
| title_short | Spherical Induced Ensembles with Symplectic Symmetry |
| title_sort | spherical induced ensembles with symplectic symmetry |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211910 |
| work_keys_str_mv | AT byunsungsoo sphericalinducedensembleswithsymplecticsymmetry AT forresterpeterj sphericalinducedensembleswithsymplecticsymmetry |