Beta-ensembles with covariance
Name
890211041-MIT.pdf
Description
Full printable version
Size
3.68 MB
Format
Adobe PDF
Checksum (MD5)
9d89be280b5f3893b37d7073a9187446
Author(s)
Dubbs, Alexander
Advisor(s)
Alan Edelman.
Date Issued
2014
Publisher
Massachusetts Institute of Technology
Abstract
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.
Description
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2014.
67
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 73-79).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
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