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 http://hdl.handle.net/10402/era.25367
 Smallest singular value of sparse random matrices
 Rivasplata, Omar D
 English

random matrices
sparse matrices
singular values
invertibility of random matrices
subGaussian random variables
compressible vectors
incompressible vectors
deviation inequalities  Jan 31, 2012 2:12 PM
 Thesis
 English
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 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 rth moment of the entries, for some r > 2.
 Doctoral
 Doctor of Philosophy
 Department of Mathematical and Statistical Sciences
 Mathematics
 Spring 2012

Nicole TomczakJaegermann (Mathematical and Statistical Sciences)
Alexander Litvak (Mathematical and Statistical Sciences) 
Vladimir Troitsky (Mathematical and Statistical Sciences)
Vlad Yaskin (Mathematical and Statistical Sciences)
Alexander Penin (Physics)
Mark Meckes (External Examiner)
Faculty of Graduate Studies and Research
Theses and Dissertations Spring 2009 to present
Department of Mathematical and Statistical Sciences
Theses and Dissertations Spring 2009 to present
Department of Mathematical and Statistical Sciences
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