Computing the Tracy-Widom Distribution for Arbitrary > 0
We compute the Tracy-Widom distribution describing the asymptotic distribution of the largest eigenvalue of a large random matrix by solving a boundary-value problem posed by Bloemendal in his Ph.D. Thesis (2011). The distribution is computed in two ways. The first method is a second-order finite-di...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2024 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2024
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/212118 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Computing the Tracy-Widom Distribution for Arbitrary > 0. Thomas Trogdon and Yiting Zhang. SIGMA 20 (2024), 005, 26 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862543427614277632 |
|---|---|
| author | Trogdon, Thomas Zhang, Yiting |
| author_facet | Trogdon, Thomas Zhang, Yiting |
| citation_txt | Computing the Tracy-Widom Distribution for Arbitrary > 0. Thomas Trogdon and Yiting Zhang. SIGMA 20 (2024), 005, 26 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We compute the Tracy-Widom distribution describing the asymptotic distribution of the largest eigenvalue of a large random matrix by solving a boundary-value problem posed by Bloemendal in his Ph.D. Thesis (2011). The distribution is computed in two ways. The first method is a second-order finite-difference method, and the second is a highly accurate Fourier spectral method. Since is simply a parameter in the boundary-value problem, any > 0 can be used, in principle. The limiting distribution of the th largest eigenvalue can also be computed. Our methods are available in the Julia package TracyWidomBeta.jl.
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| first_indexed | 2026-03-12T22:17:52Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212118 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-12T22:17:52Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Trogdon, Thomas Zhang, Yiting 2026-01-28T13:58:06Z 2024 Computing the Tracy-Widom Distribution for Arbitrary > 0. Thomas Trogdon and Yiting Zhang. SIGMA 20 (2024), 005, 26 pages 1815-0659 2020 Mathematics Subject Classification: 65M06; 60B20; 60H25 arXiv:2304.04951 https://nasplib.isofts.kiev.ua/handle/123456789/212118 https://doi.org/10.3842/SIGMA.2024.005 We compute the Tracy-Widom distribution describing the asymptotic distribution of the largest eigenvalue of a large random matrix by solving a boundary-value problem posed by Bloemendal in his Ph.D. Thesis (2011). The distribution is computed in two ways. The first method is a second-order finite-difference method, and the second is a highly accurate Fourier spectral method. Since is simply a parameter in the boundary-value problem, any > 0 can be used, in principle. The limiting distribution of the th largest eigenvalue can also be computed. Our methods are available in the Julia package TracyWidomBeta.jl. This work is partially supported by NSFDMS-1945652. The authors would like to thank the anonymous referees for their helpful comments and suggestions, which have significantly contributed to the clarity of this paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Computing the Tracy-Widom Distribution for Arbitrary > 0 Article published earlier |
| spellingShingle | Computing the Tracy-Widom Distribution for Arbitrary > 0 Trogdon, Thomas Zhang, Yiting |
| title | Computing the Tracy-Widom Distribution for Arbitrary > 0 |
| title_full | Computing the Tracy-Widom Distribution for Arbitrary > 0 |
| title_fullStr | Computing the Tracy-Widom Distribution for Arbitrary > 0 |
| title_full_unstemmed | Computing the Tracy-Widom Distribution for Arbitrary > 0 |
| title_short | Computing the Tracy-Widom Distribution for Arbitrary > 0 |
| title_sort | computing the tracy-widom distribution for arbitrary > 0 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212118 |
| work_keys_str_mv | AT trogdonthomas computingthetracywidomdistributionforarbitrary0 AT zhangyiting computingthetracywidomdistributionforarbitrary0 |