Beta-ensembles with covariance
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2014.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2014
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| Online Access: | http://hdl.handle.net/1721.1/90185 |
| _version_ | 1826206037890301952 |
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| author | Dubbs, Alexander |
| author2 | Alan Edelman. |
| author_facet | Alan Edelman. Dubbs, Alexander |
| author_sort | Dubbs, Alexander |
| collection | MIT |
| description | Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2014. |
| first_indexed | 2024-09-23T13:23:01Z |
| format | Thesis |
| id | mit-1721.1/90185 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T13:23:01Z |
| publishDate | 2014 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/901852019-04-10T15:26:17Z Beta-ensembles with covariance Dubbs, Alexander Alan Edelman. 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, 2014. 67 Cataloged from PDF version of thesis. Includes bibliographical references (pages 73-79). This thesis presents analytic samplers for the [beta]-Wishart and [beta]-MANOVA ensembles with diagonal covariance. These generalize the [beta]-ensembles of Dumitriu-Edelman, Lippert, Killip-Nenciu, Forrester-Rains, and Edelman-Sutton, as well as the classical [beta] = 1, 2,4 ensembles of James, Li-Xue, and Constantine. Forrester discovered a sampler for the [beta]-Wishart ensemble around the same time, although our proof has key differences. We also derive the largest eigenvalue pdf for the [beta]-MANOVA case. In infinite-dimensional random matrix theory, we find the moments of the Wachter law, and the Jacobi parameters and free cumulants of the McKay and Wachter laws. We also present an algorithm that uses complex analysis to solve "The Moment Problem." It takes the first batch of moments of an analytic, compactly-supported distribution as input, and it outputs a fine discretization of that distribution. by Alexander Dubbs. Ph. D. 2014-09-19T21:44:48Z 2014-09-19T21:44:48Z 2014 2014 Thesis http://hdl.handle.net/1721.1/90185 890211041 eng M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 79 pages application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Dubbs, Alexander Beta-ensembles with covariance |
| title | Beta-ensembles with covariance |
| title_full | Beta-ensembles with covariance |
| title_fullStr | Beta-ensembles with covariance |
| title_full_unstemmed | Beta-ensembles with covariance |
| title_short | Beta-ensembles with covariance |
| title_sort | beta ensembles with covariance |
| topic | Mathematics. |
| url | http://hdl.handle.net/1721.1/90185 |
| work_keys_str_mv | AT dubbsalexander betaensembleswithcovariance |