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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2304.04951 |
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| _version_ | 1866911756564037632 |
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| author | Trogdon, Thomas Zhang, Yiting |
| author_facet | Trogdon, Thomas Zhang, Yiting |
| contents | 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 $β$ is simply a parameter in the boundary-value problem, any $β> 0$ can be used, in principle. The limiting distribution of the $n$th largest eigenvalue can also be computed. Our methods are available in the Julia package TracyWidomBeta.jl. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_04951 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Computing the Tracy-Widom Distribution for Arbitrary $β>0$ Trogdon, Thomas Zhang, Yiting Numerical Analysis Mathematical Physics Probability 65M06, 60B20, 60H25 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 $β$ is simply a parameter in the boundary-value problem, any $β> 0$ can be used, in principle. The limiting distribution of the $n$th largest eigenvalue can also be computed. Our methods are available in the Julia package TracyWidomBeta.jl. |
| title | Computing the Tracy-Widom Distribution for Arbitrary $β>0$ |
| topic | Numerical Analysis Mathematical Physics Probability 65M06, 60B20, 60H25 |
| url | https://arxiv.org/abs/2304.04951 |