Freezing Limits for Beta-Cauchy Ensembles
Bessel processes associated with the root systems ₋₁ and describe interacting particle systems with particles on ℝ; they form dynamic versions of the classical -Hermite and Laguerre ensembles. In this paper, we study corresponding Cauchy processes constructed via some subordination. This leads to...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2022 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2022
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211719 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Freezing Limits for Beta-Cauchy Ensembles. Michael Voit. SIGMA 18 (2022), 069, 25 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862728872873689088 |
|---|---|
| author | Voit, Michael |
| author_facet | Voit, Michael |
| citation_txt | Freezing Limits for Beta-Cauchy Ensembles. Michael Voit. SIGMA 18 (2022), 069, 25 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Bessel processes associated with the root systems ₋₁ and describe interacting particle systems with particles on ℝ; they form dynamic versions of the classical -Hermite and Laguerre ensembles. In this paper, we study corresponding Cauchy processes constructed via some subordination. This leads to -Cauchy ensembles in both cases with explicit distributions. For these distributions, we derive central limit theorems for fixed in the freezing regime, i.e., when the parameters tend to infinity. The results are closely related to corresponding known freezing results for -Hermite and Laguerre ensembles and for Bessel processes.
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| first_indexed | 2026-04-17T14:38:04Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211719 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-04-17T14:38:04Z |
| publishDate | 2022 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Voit, Michael 2026-01-09T12:44:33Z 2022 Freezing Limits for Beta-Cauchy Ensembles. Michael Voit. SIGMA 18 (2022), 069, 25 pages 1815-0659 2020 Mathematics Subject Classification: 60F05; 60B20; 70F10; 82C22; 33C45 arXiv:2205.08153 https://nasplib.isofts.kiev.ua/handle/123456789/211719 https://doi.org/10.3842/SIGMA.2022.069 Bessel processes associated with the root systems ₋₁ and describe interacting particle systems with particles on ℝ; they form dynamic versions of the classical -Hermite and Laguerre ensembles. In this paper, we study corresponding Cauchy processes constructed via some subordination. This leads to -Cauchy ensembles in both cases with explicit distributions. For these distributions, we derive central limit theorems for fixed in the freezing regime, i.e., when the parameters tend to infinity. The results are closely related to corresponding known freezing results for -Hermite and Laguerre ensembles and for Bessel processes. The author would like to thank the anonymous referees for their numerous comments, which improved the paper considerably. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Freezing Limits for Beta-Cauchy Ensembles Article published earlier |
| spellingShingle | Freezing Limits for Beta-Cauchy Ensembles Voit, Michael |
| title | Freezing Limits for Beta-Cauchy Ensembles |
| title_full | Freezing Limits for Beta-Cauchy Ensembles |
| title_fullStr | Freezing Limits for Beta-Cauchy Ensembles |
| title_full_unstemmed | Freezing Limits for Beta-Cauchy Ensembles |
| title_short | Freezing Limits for Beta-Cauchy Ensembles |
| title_sort | freezing limits for beta-cauchy ensembles |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211719 |
| work_keys_str_mv | AT voitmichael freezinglimitsforbetacauchyensembles |