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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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Table of 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.