Source: Dissertation Abstracts International, Volume: 79-10(E), Section: B.
Advisors: Alice Guionnet.
Özet:
In this thesis, we investigate the local and global properties of the eigenvalues of beta-ensembles. A lot of attention has been drawn recently on the universal properties of beta-ensembles, and how their local statistics relate to those of Gaussian ensembles. We use transport methods to prove universality of the eigenvalue gaps in the bulk and at the edge, in the single cut and tnulticut regimes. In a different direction, we also prove Central Limit Theorems for the linear statistics of beta-ensembles at the macroscopic and mesoscopic scales. (Copies available exclusively from MIT Libraries, libraries.mit.edu/docs - docs mit.edu).