Fluctuation moments induced by asymptotically liberating random matrix ensembles
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Authors
Vazquez Becerra, Josue
Date
Type
thesis
Language
eng
Keyword
Free probability , Random matrices , Fluctuation moments , Discrete Fourier Transform matrix
Alternative Title
Abstract
The topics covered in this thesis belong to the theories of free probability and random matrices. Random matrix ensembles composed of independent Haar-unitary random matrices, or independent Haar-orthogonal random matrices, are known to be asymptotically liberating, they give rise to asymptotic free independence when used for conjugation of constant matrices. G. Anderson and B. Farrel showed that certain family of discrete random unitary matrices can actually be used to same end.
We investigate fluctuation moments and higher order moments induced on constant matrices by conjugation with asymptotically liberating random matrix ensembles. We show for the first time that the fluctuation moments associated to second order free independence can be obtained from conjugation with an ensemble consisting of signed permutation matrices and the Discrete Fourier Transform matrix. We also determine fluctuation moments induced by various related ensembles where we do not get known expressions but others related to traffic free independence.
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Queen's University's Thesis/Dissertation Non-Exclusive License for Deposit to QSpace and Library and Archives Canada
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Copying and Preserving Your Thesis
This publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner.
Attribution-NonCommercial 3.0 United States
ProQuest PhD and Master's Theses International Dissemination Agreement
Intellectual Property Guidelines at Queen's University
Copying and Preserving Your Thesis
This publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner.
Attribution-NonCommercial 3.0 United States