### Abstract

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.

Original language | Undefined |
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Journal | arXiv |

State | Published - Apr 15 2014 |

### Keywords

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

## Cite this

Arous, G. B., & Dang, K. (2014). Smallest Singular Value for Perturbations of Random Permutation Matrices.

*arXiv*.