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dc.contributor.advisorAlice Guionnet.en_US
dc.contributor.authorBekerman, Florenten_US
dc.contributor.otherMassachusetts Institute of Technology. Department of Mathematics.en_US
dc.date.accessioned2018-05-23T16:29:49Z
dc.date.available2018-05-23T16:29:49Z
dc.date.copyright2018en_US
dc.date.issued2018en_US
dc.identifier.urihttp://hdl.handle.net/1721.1/115676
dc.descriptionThesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2018.en_US
dc.descriptionIn title on title page, "[beta]" appears as the lower case Greek letter. Cataloged from PDF version of thesis.en_US
dc.descriptionIncludes bibliographical references (pages 137-142).en_US
dc.description.abstractIn 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.en_US
dc.description.statementofresponsibilityby Florent Bekerman.en_US
dc.format.extent142 pagesen_US
dc.language.isoengen_US
dc.publisherMassachusetts Institute of Technologyen_US
dc.rightsMIT 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.en_US
dc.rights.urihttp://dspace.mit.edu/handle/1721.1/7582en_US
dc.subjectMathematics.en_US
dc.titleTransport methods and universality for [beta]-ensemblesen_US
dc.typeThesisen_US
dc.description.degreePh. D.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mathematics
dc.identifier.oclc1036985584en_US


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