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Smallest singular value of sparse random matrices Open Access


Other title
incompressible vectors
deviation inequalities
sparse matrices
random matrices
singular values
compressible vectors
invertibility of random matrices
sub-Gaussian random variables
Type of item
Degree grantor
University of Alberta
Author or creator
Rivasplata, Omar D
Supervisor and department
Alexander Litvak (Mathematical and Statistical Sciences)
Nicole Tomczak-Jaegermann (Mathematical and Statistical Sciences)
Examining committee member and department
Vlad Yaskin (Mathematical and Statistical Sciences)
Alexander Penin (Physics)
Vladimir Troitsky (Mathematical and Statistical Sciences)
Mark Meckes (External Examiner)
Department of Mathematical and Statistical Sciences
Date accepted
Graduation date
Doctor of Philosophy
Degree level
In this thesis probability estimates on the smallest singular value of random matrices with independent entries are extended to a class of sparse random matrices. We show that one can relax a previously used condition of uniform boundedness of the variances from below. This allows us to consider matrices with null entries or, more generally, with entries having small variances. Our results do not assume identical distribution of the entries of a random matrix, and help to clarify the role of the variances in the corresponding estimates. We also show that it is enough to require boundedness from above of the r-th moment of the entries, for some r > 2.
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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