Beta-ensembles with covariance

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.

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mathematics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2014

Author dc:creator

• Dubbs, Alexander

Advisor dc:contributor.advisor

• Alan Edelman.

• Mathematics.

Statement dc:rights

• 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.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/90185

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/90185