Transport methods and universality for [beta]-ensembles

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2018.In title on title page, "[beta]" appears as the lower case Greek letter. Cataloged from PDF version of thesis.Includes bibliographical references (pages 137-142).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 multicut regimes. In a different direction, we also prove Central Limit Theorems for the linear statistics of [beta]-ensembles at the macroscopic and mesoscopic scales.by Florent Bekerman.Ph. D