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 investi...
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ndltd-MIT-oai-dspace.mit.edu-1721.1-1156762019-05-02T16:20:17Z Transport methods and universality for [beta]-ensembles Bekerman, Florent Alice Guionnet. Massachusetts Institute of Technology. Department of Mathematics. Massachusetts Institute of Technology. Department of Mathematics. Mathematics. 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. 2018-05-23T16:29:49Z 2018-05-23T16:29:49Z 2018 2018 Thesis http://hdl.handle.net/1721.1/115676 1036985584 eng 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 142 pages application/pdf Massachusetts Institute of Technology |
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Mathematics. Bekerman, Florent Transport methods and universality for [beta]-ensembles |
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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. |
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Alice Guionnet. |
author_facet |
Alice Guionnet. Bekerman, Florent |
author |
Bekerman, Florent |
author_sort |
Bekerman, Florent |
title |
Transport methods and universality for [beta]-ensembles |
title_short |
Transport methods and universality for [beta]-ensembles |
title_full |
Transport methods and universality for [beta]-ensembles |
title_fullStr |
Transport methods and universality for [beta]-ensembles |
title_full_unstemmed |
Transport methods and universality for [beta]-ensembles |
title_sort |
transport methods and universality for [beta]-ensembles |
publisher |
Massachusetts Institute of Technology |
publishDate |
2018 |
url |
http://hdl.handle.net/1721.1/115676 |
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AT bekermanflorent transportmethodsanduniversalityforbetaensembles |
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