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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Бібліографічні деталі
Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2024
Автори: Trogdon, Thomas, Zhang, Yiting
Формат: Стаття
Мова:Англійська
Опубліковано: Інститут математики НАН України 2024
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

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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Резюме: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.
ISSN:1815-0659