2026-09-19T16:01:54Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/1156762026-06-17T14:46:08Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Alice Guionnet.
Bekerman, Florent
Massachusetts Institute of Technology. Department of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2018-05-23T16:29:49Z
2018-05-23T16:29:49Z
2018
2018
http://hdl.handle.net/1721.1/115676
1036985584
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.
142 pages
eng
Massachusetts Institute of Technology
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.
http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
Transport methods and universality for [beta]-ensembles
Thesis
application/pdf
false
Publication
unknown
unknown
<Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="b71b83d5-07ad-4fcf-b946-f2fb10ea6f0b">
<Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type>
<Language>eng</Language>
<Title>Transport methods and universality for [beta]-ensembles</Title>
<PublishedIn>
<Publication>
</Publication>
</PublishedIn>
<PublicationDate>2018</PublicationDate>
<Authors>
<Author>
<DisplayName>Bekerman, Florent</DisplayName>
<Affiliation>
<OrgUnit>
</OrgUnit>
</Affiliation>
</Author>
</Authors>
<Editors>
</Editors>
<Publishers>
<Publisher>
<DisplayName>Massachusetts Institute of Technology</DisplayName>
<OrgUnit />
</Publisher>
</Publishers>
<License>http://dspace.mit.edu/handle/1721.1/7582</License>
<Keyword>Mathematics.</Keyword>
<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.</Abstract>
<Access xmlns="http://purl.org/coar/access_right"
>
</Access>
</Publication>