2026-09-19T06:28:34Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/901852026-06-17T14:44:49Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Alan Edelman.
Dubbs, Alexander
Massachusetts Institute of Technology. Department of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2014-09-19T21:44:48Z
2014-09-19T21:44:48Z
2014
2014
http://hdl.handle.net/1721.1/90185
890211041
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.
79 pages
eng
Massachusetts Institute of Technology
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
Mathematics.
Beta-ensembles with covariance
Thesis
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