### 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 language | English (US) |
---|---|

Pages (from-to) | 289-314 |

Number of pages | 26 |

Journal | Israel Journal of Mathematics |

Volume | 212 |

Issue number | 1 |

DOIs | |

State | Published - May 1 2016 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

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## Cite this

*Israel Journal of Mathematics*,

*212*(1), 289-314. https://doi.org/10.1007/s11856-016-1287-8