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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
    sub-Gaussian random variables
    compressible vectors
    incompressible vectors
    deviation inequalities
  • Jan 31, 2012 2:12 PM
  • Thesis
  • English
  • Adobe PDF
  • 381368 bytes
  • 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.
  • Doctoral
  • Doctor of Philosophy
  • Department of Mathematical and Statistical Sciences
  • Mathematics
  • Spring 2012
  • Nicole Tomczak-Jaegermann (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)