The smallest singular value of random rectangular matrices with no moment assumptions on entries

Konstantin Tikhomirov

Research output: Contribution to journalArticle

10 Scopus citations

Abstract

Let δ > 1 and β > 0 be some real numbers. We prove that there are positive u, v, N 0 depending only on β and δ with the following property: for any N,n such that N ≥ max(N 0 , δ n ), any N × n random matrix A = (a ij ) with i.i.d. entries satisfying (Formula presented.) and any non-random N × n matrix B, the smallest singular value s n of A + B satisfies (Formula presented.). The result holds without any moment assumptions on the distribution of the entries of A.

Original languageEnglish (US)
Pages (from-to)289-314
Number of pages26
JournalIsrael Journal of Mathematics
Volume212
Issue number1
DOIs
StatePublished - May 1 2016

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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