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thesis.pdf (631.84 KB)
ETD Abstract Container
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On Truncations of Haar Distributed Random Matrices
Author Info
Stewart, Kathryn Lockwood
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=case1554279921382029
Abstract Details
Year and Degree
2019, Doctor of Philosophy, Case Western Reserve University, Mathematics.
Abstract
The main focus of this dissertation is the study of truncations, that is principal submatrices, of an n by n Haar-distributed random matrix. In Chapter 2, we show that a p by q truncation of a random orthogonal matrix is close in total variation distance to a p by q matrix of independent identically distributed Gaussian random variables as long as the product pq = o(n), making use of new estimates on the asymptotic means and covariances of the traces of powers of Wishart matrices. Chapter 3 considers limiting spectral measures of square truncations of a unitary matrix and develops some nonasymptotic results describing the ensemble of eigenvalues of the truncations.
Committee
Elizabeth Meckes (Advisor)
Harsh Mathur (Committee Member)
Mark Meckes (Committee Member)
Stanislaw Szarek (Committee Member)
Pages
111 p.
Subject Headings
Mathematics
Keywords
random matrices, random orthogonal matrix, random unitary matrix, central limit theorem, Wishart matrices, moments, submatrices, empirical spectral measure, Coulomb gases
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Citations
Stewart, K. L. (2019).
On Truncations of Haar Distributed Random Matrices
[Doctoral dissertation, Case Western Reserve University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=case1554279921382029
APA Style (7th edition)
Stewart, Kathryn.
On Truncations of Haar Distributed Random Matrices.
2019. Case Western Reserve University, Doctoral dissertation.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=case1554279921382029.
MLA Style (8th edition)
Stewart, Kathryn. "On Truncations of Haar Distributed Random Matrices." Doctoral dissertation, Case Western Reserve University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=case1554279921382029
Chicago Manual of Style (17th edition)
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Document number:
case1554279921382029
Download Count:
677
Copyright Info
© 2019, some rights reserved.
On Truncations of Haar Distributed Random Matrices by Kathryn Lockwood Stewart is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by Case Western Reserve University School of Graduate Studies and OhioLINK.