### Abstract

Original language | Undefined |
---|---|

Journal | arXiv |

State | Published - Apr 15 2014 |

### Keywords

- math.PR
- 15B52, 60B20, 60C05

### Cite this

*arXiv*.

**Smallest Singular Value for Perturbations of Random Permutation Matrices.** / Arous, Gérard Ben; Dang, Kim.

Research output: Contribution to journal › Article

*arXiv*.

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TY - JOUR

T1 - Smallest Singular Value for Perturbations of Random Permutation Matrices

AU - Arous, Gérard Ben

AU - Dang, Kim

N1 - 33 pages

PY - 2014/4/15

Y1 - 2014/4/15

N2 - We take a first small step to extend the validity of Rudelson-Vershynin type estimates to some sparse random matrices, here random permutation matrices. We give lower (and upper) bounds on the smallest singular value of a large random matrix D+M where M is a random permutation matrix, sampled uniformly, and D is diagonal. When D is itself random with i.i.d terms on the diagonal, we obtain a Rudelson-Vershynin type estimate, using the classical theory of random walks with negative drift.

AB - We take a first small step to extend the validity of Rudelson-Vershynin type estimates to some sparse random matrices, here random permutation matrices. We give lower (and upper) bounds on the smallest singular value of a large random matrix D+M where M is a random permutation matrix, sampled uniformly, and D is diagonal. When D is itself random with i.i.d terms on the diagonal, we obtain a Rudelson-Vershynin type estimate, using the classical theory of random walks with negative drift.

KW - math.PR

KW - 15B52, 60B20, 60C05

M3 - Article

JO - arXiv

JF - arXiv

ER -