Beta-ensembles with covariance
Massachusetts Institute of Technology. Department of Mathematics.
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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.
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2014.67Cataloged from PDF version of thesis.Includes bibliographical references (pages 73-79).
DepartmentMassachusetts Institute of Technology. Department of Mathematics.; Massachusetts Institute of Technology. Department of Mathematics
Massachusetts Institute of Technology