Transport methods and universality for [beta]-ensembles
Name
1036985584-MIT.pdf
Description
Full printable version
Size
7.77 MB
Format
Adobe PDF
Checksum (MD5)
b12d106e65e14064c00ec16dc2970ad3
Author(s)
Bekerman, Florent
Advisor(s)
Alice Guionnet.
Date Issued
2018
Publisher
Massachusetts Institute of Technology
Abstract
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.
Description
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).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission.
Persistent DSpace Link
