On the Tracy-Widomβ Distribution for β=6

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2016
• Main Authors: Grava, T., Its, A., Kapaev, A., Mezzadri, F.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2016
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/148536
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: On the Tracy-Widomβ Distribution for β=6 / T. Grava, A. Its, A. Kapaev, F. Mezzadri // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 26 назв. — англ.

We study the Tracy-Widom distribution function for Dyson's β-ensemble with β=6. The starting point of our analysis is the recent work of I. Rumanov where he produces a Lax-pair representation for the Bloemendal-Virág equation. The latter is a linear PDE which describes the Tracy-Widom functions...